Publications [#360275] of Mark Haskins

Papers Published

1. Degeratu, A; Haskins, M; Weiß, H, Mini-Workshop: Singularities in $\mathrm G_2$-geometry, Oberwolfach Reports, vol. 12 no. 1 (December, 2015), pp. 449-488, European Mathematical Society - EMS - Publishing House GmbH [doi]
   (last updated on 2026/01/14)

   Abstract:
   All currently known construction methods of smooth compact \mathrm G_2 -manifolds have been tied to certain singular \mathrm G_2 -spaces, which in Joyce’s original construction are \mathrm G_2 -orbifolds and in Kovalev’s twisted connected sum construction are complete G2-manifolds with cylindrical ends. By a slight abuse of terminology we also refer to the latter as singular \mathrm G_2 -spaces, and in fact both construction methods may be viewed as desingularization procedures. In turn, singular \mathrm G_2 -spaces comprise a (conjecturally large) part of the boundary of the moduli space of smooth compact \mathrm G_2 -manifolds, and so their deformation theory is of considerable interest. Furthermore, singular \mathrm G_2 -spaces are also important in theoretical physics. Namely, in order to have realistic low-energy physics in M-theory, one needs compact singular \mathrm G_2 -spaces with both codimension 4 and 7 singularities according to Acharya and Witten. However, the existence of such singular \mathrm G_2 -spaces is unknown at present. The aim of this workshop was to bring reserachers from special holonomy geometry, geometric analysis and theoretical physics together to exchange ideas on these questions.