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15 July 2015 G2-manifolds and associative submanifolds via semi-Fano3-folds
Alessio Corti, Mark Haskins, Johannes Nordström, Tommaso Pacini
Duke Math. J. 164(10): 1971-2092 (15 July 2015). DOI: 10.1215/00127094-3120743

Abstract

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.

Citation

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Alessio Corti. Mark Haskins. Johannes Nordström. Tommaso Pacini. "G2-manifolds and associative submanifolds via semi-Fano3-folds." Duke Math. J. 164 (10) 1971 - 2092, 15 July 2015. https://doi.org/10.1215/00127094-3120743

Information

Received: 25 June 2013; Revised: 13 August 2014; Published: 15 July 2015
First available in Project Euclid: 14 July 2015

zbMATH: 1343.53044
MathSciNet: MR3369307
Digital Object Identifier: 10.1215/00127094-3120743

Subjects:
Primary: 53C29
Secondary: 14J28, 14J32, 14J45, 53C25, 53C38

Rights: Copyright © 2015 Duke University Press

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Vol.164 • No. 10 • 15 July 2015
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