%% Books
@book{fds51656,
Author = {H. Edelsbrunner and J. Harer},
Title = {Computational Topology, An Introduction},
Year = {2008},
Abstract = {This book is an introduction to computational topology for
students in Computer Science and Mathematics. Currently 183
pages, it is in its second draft - submission for
publication is expected in Summer 2007.},
Key = {fds51656}
}
@book{fds10018,
Author = {Penner, R. C. and Harer, J. L.},
Title = {Combinatorics of train tracks},
Journal = {pp. xii+216, 1992, Princeton University Press, Princeton,
NJ},
MRNUMBER = {94b:57018},
Key = {fds10018}
}
%% Papers Published
@article{fds152560,
Author = {P. Bendich and D. Cohen-Steiner and H. Edelsbrunner and J. Harer and D. Morozov.},
Title = {Inferring local homology from sampled stratified
spaces.},
Journal = {Proc. 48th Ann. Sympos. Found. Comput. Sci.},
Pages = {536-546},
Year = {2008},
url = {http://www.cs.duke.edu/~edels/Topology/},
Abstract = {http://www.cs.duke.edu/~edels/Topology/},
Key = {fds152560}
}
@article{fds42085,
Author = {D. Cohen-Steiner and H. Edelsbrunner and J.
Harer.},
Title = {Stability of persistence diagrams.},
Journal = {Discrete Comput. Geom.},
Volume = {37},
Pages = {103-120},
Year = {2007},
Abstract = {The persistence diagram of a real-valued function on a
topological space is a multi-set of points in the extended
plane. We prove that under mild assumptions on the function,
the persistence diagram is stable: small changes in the
function imply only small changes in the diagram. We apply
this result to estimating the homology of sets in a metric
space and to comparing and classifying geometric
shapes.},
Key = {fds42085}
}
@article{fds139645,
Author = {H. Edelsbrunner and J. Harer},
Title = {Persistent homology --- a survey.},
Journal = {In Twenty Years After, eds. J. E. Goodman, J. Pach and R.
Pollack, AMS.},
Year = {2007},
url = {http://math.duke.edu/~harer/public_html/papers/survey.pdf},
Abstract = {This paper surveys the current state of the art in
computational topology. It is intended for computational
geometers and combinatorialists.},
Key = {fds139645}
}
@article{fds139643,
Author = {D. Attali and H. Edelsbrunner and J. Harer and Y.
Milokov},
Title = {Alpha-beta witness complexes},
Journal = {Proc. 10th Workshop Algor. Data Struct., 2007, Springer LNCS
4619, 386-397.},
Year = {2007},
Abstract = {This paper presents the results of extensive experiments on
the witness complexes of high dimensional point
clouds.},
Key = {fds139643}
}
@article{fds43992,
Author = {J. Harer and H. Edelsbrunner and V. Natarajan and V. Pascucci.},
Title = {Local and Global Comparison of Continuous
Functions},
Journal = {Proc. IEEE Conf. Visualization, 2004, 275-280.},
Pages = {275-280},
Year = {2004},
Abstract = {We introduce local and global comparison measures for a
collection of k <= d real-valued smooth functions on a
common d-dimensional Riemannian manifold. For k = d = 2 we
relate the measures to the set of critical points of one
function restricted to the level sets of the other. The
definition of the measures extends to piecewise linear
functions for which they are easy to compute. The
computation of the measures forms the centerpiece of a
software tool which we use to study scientific
datasets.},
Key = {fds43992}
}
@article{fds28879,
Author = {J. Harer and P. K. Agarwal and H. Edelsbrunner and Y. Wang},
Title = {Extreme elevation on a 2-manifold.},
Journal = {Proc. 20th Ann. Sympos. Comput. Geom.},
Pages = {357-365},
Year = {2004},
Abstract = {Given a smoothly embedded 2-manifold in $\Rspace^3$, we
define the elevation of a point as the height difference to
a canonically defined second point on the same manifold. Our
definition is invariant under rigid motions and can be used
to define features such as lines of discontinuous or
continuous but non-smooth elevation. We give an algorithm
for finding points of locally maximum elevation, which we
suggest mark cavities and protrusions and are useful in
matching shapes as for example in protein
docking.},
Key = {fds28879}
}
@article{fds28881,
Author = {J. Harer and H. Edelsbrunner and A. Mascarenhas and V. Pascucci},
Title = {Time-varying Reeb graphs for continuous space-time
data.},
Journal = {Proc. 20th Ann. Sympos. Comput. Geom.},
Pages = {366-372.},
Year = {2004},
Abstract = {We study the evolution of the Reeb graph of a time-varying
continuous function defined in three-dimensional space.
While maintaining the Reeb graph, we compress the evolving
sequence into a single, partially persistent data structure.
We envision this data structure as a useful tool in
visualizing real-valued space-time data obtained from
computational simulations of physical processes.},
Key = {fds28881}
}
@article{fds28882,
Author = {J. Harer and K. Cole-McLaughlin and H. Edelsbrunner and V. Natarajan and V.
Pascucci},
Title = {Loops in Reeb graphs of 2-manifolds.},
Journal = {Discrete Comput. Geom.},
Volume = {32},
Pages = {231-244.},
Year = {2004},
Abstract = {Given a Morse function f over a 2-manifold with or without
boundary, the Reeb graph is obtained by contracting the
connected components of the level sets to points. We prove
tight upper and lower bounds on the number of loops in the
Reeb graph that depend on the genus, the number of boundary
components, and whether or not the 2-manifold is orientable.
We also give an algorithm that constructs the Reeb graph in
time O(n log n$), where n is the number of edges in the
triangulation used to represent the 2-manifold and the Morse
function.},
Key = {fds28882}
}
@article{fds28883,
Author = {J. Harer and P. Agarwal and A. Collins},
Title = {HPRM: A Hierarchical PRM},
Journal = {Proc. Intl. Conf. Robotics and Automation},
Year = {2003},
Abstract = {We introduce a hierarchical variant of the probabilistic
roadmap method for motion planning. By recursively refining
an initially sparse sampling in neighborhoods of the
C-obstacle boundary, our algorithm generates a smaller
roadmap that is more likely to find narrow passages than
uniform sampling. We analyze the failure probability and
computation time, relating them to path length, path
clearance, roadmap size, recursion depth, and a local
property of the free space. The approach is general, and can
be tailored to any variety of robots. In particular, we
describe algorithmic details for a planar articulated
arm.},
Key = {fds28883}
}
@article{fds29134,
Author = {J. Harer and H. Edelsbrunner and V. Natarajan and V. Pascucci.},
Title = {Morse-Smale complexes for piecewise linear
3-manifolds.},
Journal = {Proc. 19th Ann. Sympos. Comput. Geom.},
Pages = {361-370.},
Year = {2003},
Abstract = {We define the Morse complex of a Morse function over a
3-manifold as the overlay of the stable and unstable
manifolds of all critical points. In the generic case, its
3-dimensional cells are shaped like crystals and are
separated by quadrangular faces. In this paper, we give a
combinatorial algorithm for constructing such complexes for
piecewise linear data. We also describe how to measure the
persistence of the critical points and how to use that
measurement to simplify the complex.},
Key = {fds29134}
}
@article{fds29135,
Author = {J. Harer and H. Edelsbrunner.},
Title = {Jacobi sets of multiple Morse functions.},
Journal = {Foundations of Computational Mathematics, Minneapolis, eds.
F. Cucker, R. DeVore, P. Olver and E. Sueli, Cambridge Univ.
Press, England,},
Pages = {37-57},
Year = {2002},
Abstract = {The Jacobi set of two Morse functions defined on a common
d-manifold is the set of critical points of the restrictions
of one function to the level sets of the other function.
Equivalently, it is the set of points where the gradients of
the functions are parallel. For a generic pair of Morse
functions, the Jacobi set is a smoothly embedded 1-manifold.
We give a polynomial-time algorithm that computes the
piecewise linear analog of the Jacobi set for functions
specified at the vertices of a triangulation, and we
generalize all results to more than two but at most d Morse
functions.},
Key = {fds29135}
}
@article{fds10034,
Author = {P. Agarwal and A. Collins and J. Harer},
Title = {Minimal Trap Design},
Journal = {Proceedings of the 2001 IEEE International Conference on
Robotics and Automation (ICRA),},
Year = {2001},
Abstract = {This paper addresses the issue of trap design for
sensor-less automated assembly. First we present a simple
algorithm that determines in O(nm \alpha(nm)log(nm)) time
whether an n-sided polygon part will fall through an m-sided
polygonal trap. We then introduce the notion of a minimal
trap for a polygon part, and develop an algorithm to design
a family of minimal feeders built from these traps. The
algorithm runs in O(k n^{3+\epsilon}) time, where k is the
number of stable orientations of P. Moreover, it is complete
in the sense that we can always find a feeder, provide that
one exists, that rejects and supports any chosen poses of
the part.},
Key = {fds10034}
}
@article{fds10033,
Author = {H. Edelsbrunner and J. Harer and A. Zomorodian},
Title = {Hierarchical Morse complexes for piecewise linear
2-manifolds},
Journal = {Proc. 17th Sympos. Comput. Geom. 2001, 70-79.},
Abstract = {We present algorithms for constructing a hierarchy of
increasingly coarse Morse-Smale complexes that decompose a
piecewise linear 2-manifold. While these complexes are
defined only in the smooth category, we extend the
construction to the piecewise linear category by ensuring
structural integrity and simulating differentiability. We
then simplify Morse-Smale complexes by canceling pairs of
critical points in order of increasing persistence.},
Key = {fds10033}
}
@article{fds10016,
Author = {Goulden, I. P. and Harer, J. L. and Jackson, D.
M.},
Title = {A geometric parametrization for the virtual Euler
characteristics of the moduli spaces of real and complex
algebraic curves},
Journal = {Trans. Amer. Math. Soc., vol. 353, no. 11, pp. 4405--4427
(electronic), 2001},
MRNUMBER = {1851176},
Key = {fds10016}
}
@article{fds10017,
Author = {Harer, John L.},
Title = {The rational Picard group of the moduli space of Riemann
surfaces with spin structure},
Journal = {Mapping class groups and moduli spaces of Riemann surfaces
(Gottingen, 1991/Seattle, WA, 1991), pp. 107--136, 1993,
Amer. Math. Soc., Providence, RI},
MRNUMBER = {94h:14008},
Key = {fds10017}
}
@article{fds10019,
Author = {Harer, John},
Title = {The third homology group of the moduli space of
curves},
Journal = {Duke Math. J., vol. 63, no. 1, pp. 25--55,
1991},
MRNUMBER = {92d:57012},
Key = {fds10019}
}
@article{fds10020,
Author = {Harer, John L.},
Title = {Stability of the homology of the moduli spaces of Riemann
surfaces with spin structure},
Journal = {Math. Ann., vol. 287, no. 2, pp. 323--334,
1990},
MRNUMBER = {91e:57002},
Key = {fds10020}
}
@article{fds10021,
Author = {Harer, John L.},
Title = {The cohomology of the moduli space of curves},
Journal = {Theory of moduli (Montecatini Terme, 1985), pp. 138--221,
1988, Springer, Berlin},
MRNUMBER = {90a:32026},
Key = {fds10021}
}
@article{fds10022,
Author = {Harer, John and Kas, Arnold and Kirby, Robion},
Title = {Handlebody decompositions of complex surfaces},
Journal = {Mem. Amer. Math. Soc., vol. 62, no. 350, pp. iv+102,
1986},
MRNUMBER = {88e:57030},
Key = {fds10022}
}
@article{fds10023,
Author = {Harer, J. and Zagier, D.},
Title = {The Euler characteristic of the moduli space of
curves},
Journal = {Invent. Math., vol. 85, no. 3, pp. 457--485,
1986},
MRNUMBER = {87i:32031},
Key = {fds10023}
}
@article{fds10025,
Author = {Harer, John L.},
Title = {The virtual cohomological dimension of the mapping class
group of an orientable surface},
Journal = {Invent. Math., vol. 84, no. 1, pp. 157--176,
1986},
MRNUMBER = {87c:32030},
Key = {fds10025}
}
@article{fds10024,
Author = {Harer, John L.},
Title = {Stability of the homology of the mapping class groups of
orientable surfaces},
Journal = {Ann. of Math. (2), vol. 121, no. 2, pp. 215--249,
1985},
MRNUMBER = {87f:57009},
Key = {fds10024}
}
@article{fds10026,
Title = {Geometry and topology},
Journal = {Proceedings of the special year held at the University of
Maryland, College Park, Md., 1983/84, edited by Alexander,
J. and Harer, J., pp. vi+292, 1985, Springer-Verlag,
Berlin},
MRNUMBER = {87a:57003},
Key = {fds10026}
}
@article{fds10027,
Author = {Harer, John},
Title = {The homology of the mapping class group and its connection
to surface bundles over surfaces},
Journal = {Four-manifold theory (Durham, N.H., 1982), pp. 311--314,
1984, Amer. Math. Soc., Providence, RI},
MRNUMBER = {86c:57010},
Key = {fds10027}
}
@article{fds10028,
Author = {Harer, John},
Title = {The second homology group of the mapping class group of an
orientable surface},
Journal = {Invent. Math., vol. 72, no. 2, pp. 221--239,
1983},
MRNUMBER = {84g:57006},
Key = {fds10028}
}
@article{fds10029,
Author = {Harer, John},
Title = {Representing elements of pi1(M3)
by fibred knots},
Journal = {Math. Proc. Cambridge Philos. Soc., vol. 92, no. 1, pp.
133--138, 1982},
MRNUMBER = {83j:57005},
Key = {fds10029}
}
@article{fds10031,
Author = {Harer, John},
Title = {How to construct all fibered knots and links},
Journal = {Topology, vol. 21, no. 3, pp. 263--280, 1982},
MRNUMBER = {83e:57007},
Key = {fds10031}
}
@article{fds10030,
Author = {Casson, Andrew J. and Harer, John L.},
Title = {Some homology lens spaces which bound rational homology
balls},
Journal = {Pacific J. Math., vol. 96, no. 1, pp. 23--36,
1981},
MRNUMBER = {83h:57013},
Key = {fds10030}
}
@article{fds10032,
Author = {Harer, John},
Title = {On handlebody structures for hypersurfaces in
C3 and CP3},
Journal = {Math. Ann., vol. 238, no. 1, pp. 51--58,
1978},
MRNUMBER = {80d:57020},
Key = {fds10032}
}
%% Papers Accepted
@article{fds152558,
Author = {D. Cohen-Steiner and H. Edelsbrunner and J. Harer and D.
Morozov.},
Title = {Persistent homology for kernels, images, and
cokernels.},
Journal = {Proc. Sympos. Discret Alg.},
Year = {2009},
url = {http://www.cs.duke.edu/~edels/Topology/},
Abstract = {The persistence algorithms are extended to the study of
kernels and images of homology maps. Applications include
the study of stratifications of point clouds.},
Key = {fds152558}
}
@article{fds152559,
Author = {D. Cohen-Steiner and H. Edelsbrunner and J. Harer and Y.
Mileyko.},
Title = {Lipschitz functions have L_p-stable persistence.},
Journal = {Foundations of Computional Mathematics},
Year = {2008},
url = {http://www.cs.duke.edu/~edels/Topology/},
Abstract = {This paper shows that persistence diagrams of Lipschitz
functions are stable in a stronger sense than proved in the
paper by Cohen-Steiner, Edelsbrunner and Harer. The stronger
version is more useful in the study of gene expression
data.},
Key = {fds152559}
}
@article{fds152561,
Author = {D. Cohen-Steiner and H. Edelsbrunner and J.
Harer.},
Title = {Extending persistence using Poincare and Lefschetz
duality.},
Journal = {Found. Comput. Math.},
Year = {2008},
url = {http://www.cs.duke.edu/~edels/Topology/},
Abstract = {We extend the methods of persistence and persistence
diagrams to essential homology classes using Poincare'
duality. We show that this extended definition satisfies
duality and symmetry compatible with usual persistence, find
a fast algorithm to compute it and discuss a variety of
applications including the extension of the elevation
function which is used to establish initial placements in
protein docking prediction.},
Key = {fds152561}
}
%% Papers Submitted
@article{fds28884,
Author = {G. Bini and J. Harer},
Title = {The Regular and Orbifold Euler Characteristics of the
Compactified Moduli Space of Curves},
Journal = {Topology},
Year = {2005},
Key = {fds28884}
}
%% Preprints
@article{fds152566,
Author = {P. Bendich and J. Harer and H. King},
Title = {Persistent Intersection Homology},
Year = {2008},
Key = {fds152566}
}
@article{fds152569,
Author = {Mehak Aziz and Siobhan M. Brady and David Orlando and Appu Kuruvilla and Scott Spillias and José R. Dinneny and Terri A. Long and John Harer and Uwe Ohler and Philip N. Benfey},
Title = {Gene Expression Clustering Analysis: How to Choose the Best
Parameters and Clustering Algorithm},
Year = {2008},
Abstract = {This paper is the result of a summer research project
supported by the Howard Hughes summer program in systems
biology.},
Key = {fds152569}
}
@article{fds152571,
Author = {A. HB and J. Harer},
Title = {Persistent Steifel Whitney Classes},
Year = {2008},
Abstract = {Cohomology classes are used in Algebraic Topology as a tool
that computes the complexity of n-plane bundles over a
manifold. This paper introduces a method of including a
general cohomology class into study and practice of
Persistence for homology. Using a combinatorial formula, we
illustrate our new algorithm for Stiefel-Whitney
classes.},
Key = {fds152571}
}
@article{fds51476,
Author = {P. Bendich and J. Harer},
Title = {Persistence for Intersection Homology - Theoretical
Foundations},
Year = {2008},
Abstract = {We show that the theory of persistence extends naturally to
intersection homology and give a fast algorithm to compute
it. We also describe a methodology based on local-systems
for characterizing when a point cloud has the structure of a
stratified space.},
Key = {fds51476}
}
@article{fds51657,
Author = {H. Edelsbrunner and J. Harer and A. Patel},
Title = {Reeb Surfaces},
Year = {2008},
Abstract = {This paper studies a generalization of the Reeb graph called
the Reeb surface. It characterizes the surface and gives an
efficient algorithm for its computation.},
Key = {fds51657}
}
@article{fds139649,
Author = {P. Bendich and J. Harer},
Title = {Elevation for singular spaces using persistent intersection
homology},
Year = {2007},
Key = {fds139649}
}
@article{fds8935,
Author = {John Harer},
Title = {Algorithms for Enumerating Triangulations and Other Maps in
Surfaces},
Journal = {1998},
Key = {fds8935}
}
@article{fds8938,
Author = {John Harer},
Title = {An Alternative Approach to Trap Design for Vibratory Bowl
Feeders},
Journal = {1998},
Key = {fds8938}
}
@article{fds8940,
Author = {John Harer},
Title = {The Euler Characteristic of the Deligne-Mumford
Compactification of the Moduli Space of Curves},
Journal = {1996},
Key = {fds8940}
}
%% Other
@article{fds29132,
Author = {J. Harer and H. Edelsbrunner},
Title = {Persistent Morse Complex Segmentation of a
3-Manifold},
Journal = {Raindrop Geomagic Technical Report},
Volume = {066},
Year = {2004},
Abstract = {We describe a new algorithm for segmenting 3-dimensional
medical imaging data, which we abstract as continuous
functions on 3-manifolds. The algorithm is related to
watershed algorithms developed in image processing but is
closer to its mathematical roots, which are Morse theory and
homological algebra. It allows for the implicit treatment of
its mathematical foundations with the computational
efficiency of image processing.},
Key = {fds29132}
}
|
| 
Mathematics Department