G2-Manifolds and associative submanifolds via semi-fano 3-folds

Alessio Corti, Mark Haskins, Johannes Nordström, Tommaso Pacini

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We construct many new topological types of compact G2-manifolds, that is, Riemannian 7-manifolds with holonomy group G2. To achieve this we extend the twisted connected sum construction first developed by Kovalev and apply it to the large class of asymptotically cylindrical Calabi-Yau 3-folds built from semi-Fano 3-folds constructed previously by the authors. In many cases we determine the diffeomorphism type of the underlying smooth 7-manifolds completely; we find that many 2-connected 7-manifolds can be realized as twisted connected sums in a variety of ways, raising questions about the global structure of the moduli space of G2-metrics. Many of the G2-manifolds we construct contain compact rigid associative 3-folds, which play an important role in the higher-dimensional enumerative geometry (gauge theory/ calibrated submanifolds) approach to defining deformation invariants of G2-metrics. By varying the semi-Fanos used to build different G2-metrics on the same 7-manifold we can change the number of rigid associative 3-folds we produce.

Original languageEnglish
Pages (from-to)1971-2092
Number of pages122
JournalDuke Mathematical Journal
Issue number10
Early online date14 Jul 2015
Publication statusPublished - 15 Jul 2015

ASJC Scopus subject areas

  • Mathematics(all)


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