Math @ Duke
Publications [#29135] of John Harer
- with H. Edelsbrunner., Jacobi sets of multiple Morse functions.,
Foundations of Computational Mathematics, Minneapolis, eds. F. Cucker, R. DeVore, P. Olver and E. Sueli, Cambridge Univ. Press, England,
(last updated on 2004/12/15)
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.
Duke University, Box 90320
Durham, NC 27708-0320