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

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Corti, A; Haskins, M; Nordström, J; Pacini, T

Published Date

  • January 1, 2015

Published In

Volume / Issue

  • 164 / 10

Start / End Page

  • 1971 - 2092

International Standard Serial Number (ISSN)

  • 0012-7094

Digital Object Identifier (DOI)

  • 10.1215/00127094-3120743

Citation Source

  • Scopus