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Mini-Workshop: Singularities in $\mathrm G_2$-geometryAnda Degeratu, Mark Haskins and Hartmut Weiß (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.
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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