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

Publication ,  Journal Article
Corti, A; Haskins, M; Nordström, J; Pacini, T
Published in: Duke Mathematical Journal
January 1, 2015

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.

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Published In

Duke Mathematical Journal

DOI

ISSN

0012-7094

Publication Date

January 1, 2015

Volume

164

Issue

10

Start / End Page

1971 / 2092

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

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Corti, A., Haskins, M., Nordström, J., & Pacini, T. (2015). G2-Manifolds and associative submanifolds via semi-fano 3-folds. Duke Mathematical Journal, 164(10), 1971–2092. https://doi.org/10.1215/00127094-3120743
Corti, A., M. Haskins, J. Nordström, and T. Pacini. “G2-Manifolds and associative submanifolds via semi-fano 3-folds.” Duke Mathematical Journal 164, no. 10 (January 1, 2015): 1971–2092. https://doi.org/10.1215/00127094-3120743.
Corti A, Haskins M, Nordström J, Pacini T. G2-Manifolds and associative submanifolds via semi-fano 3-folds. Duke Mathematical Journal. 2015 Jan 1;164(10):1971–2092.
Corti, A., et al. “G2-Manifolds and associative submanifolds via semi-fano 3-folds.” Duke Mathematical Journal, vol. 164, no. 10, Jan. 2015, pp. 1971–2092. Scopus, doi:10.1215/00127094-3120743.
Corti A, Haskins M, Nordström J, Pacini T. G2-Manifolds and associative submanifolds via semi-fano 3-folds. Duke Mathematical Journal. 2015 Jan 1;164(10):1971–2092.
Journal cover image

Published In

Duke Mathematical Journal

DOI

ISSN

0012-7094

Publication Date

January 1, 2015

Volume

164

Issue

10

Start / End Page

1971 / 2092

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics