## Mini-Workshop: Singularities in G2-geometry

 dc.date.accessioned 2019-10-24T15:02:03Z dc.date.available 2019-10-24T15:02:03Z dc.date.issued 2015 dc.identifier.uri http://publications.mfo.de/handle/mfo/3453 dc.description.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. dc.title Mini-Workshop: Singularities in G2-geometry dc.identifier.doi 10.14760/OWR-2015-8 local.series.id OWR-2015-8 local.subject.msc 83 local.subject.msc 58 local.subject.msc 53 local.sortindex 893 local.date-range 08 Feb - 14 Feb 2015 local.workshopcode 1507c local.workshoptitle Mini-Workshop: Singularities in G2-geometry local.organizers Anda Degeratu, Freiburg; Mark Haskins, London; Hartmut Weiss, München/Kiel local.report-name Workshop Report 2015,8 local.opc-photo-id 1507c local.publishers-doi 10.4171/OWR/2015/8 local.ems-reference 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
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