Oberwolfach Reports

Full-Text PDF (400 KB) | Introduction as PDF | Metadata | Table of Contents | OWR summary
Volume 12, Issue 1, 2015, pp. 449–488
DOI: 10.4171/OWR/2015/8

Mini-Workshop: Singularities in $\mathrm G_2$-geometry

Anda Degeratu[1], Mark Haskins[2] and Hartmut Weiß[3]

(1) Universität Freiburg, Germany
(2) Imperial College London, UK
(3) Christian-Albrechts-Universität zu Kiel, Germany

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.

No keywords available for this article.

Degeratu Anda, Haskins Mark, Weiß Hartmut: Mini-Workshop: Singularities in $\mathrm G_2$-geometry. Oberwolfach Rep. 12 (2015), 449-488. doi: 10.4171/OWR/2015/8