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• W3125411906 abstract "We construct many new topological types of compact G 2 -manifolds, that is, Riemannian 7 -manifolds with holonomy group G 2 . 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 G 2 -metrics. Many of the G 2 -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 G 2 -metrics. By varying the semi-Fanos used to build different G 2 -metrics on the same 7 -manifold we can change the number of rigid associative 3 -folds we produce." @default.
• W3125411906 created "2021-02-01" @default.
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• W3125411906 date "2015-07-15" @default.
• W3125411906 modified "2023-10-01" @default.
• W3125411906 title "G 2 -manifolds and associative submanifolds via semi-Fano 3 -folds" @default.
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• W3125411906 doi "https://doi.org/10.1215/00127094-3120743" @default.
• W3125411906 hasPublicationYear "2015" @default.
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