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G(2)-manifold and associative submanifolds via semi-fano 3-folds

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Title: G(2)-manifold and associative submanifolds via semi-fano 3-folds
Authors: Corti, A
Haskins, M
Nordstroem, J
Pacini, T
Item Type: Journal Article
Abstract: We construct many new topological types of compact G2G2-manifolds, that is, Riemannian 77-manifolds with holonomy group G2G2. 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 33-folds built from semi-Fano 33-folds constructed previously by the authors. In many cases we determine the diffeomorphism type of the underlying smooth 77-manifolds completely; we find that many 22-connected 77-manifolds can be realized as twisted connected sums in a variety of ways, raising questions about the global structure of the moduli space of G2G2-metrics. Many of the G2G2-manifolds we construct contain compact rigid associative 33-folds, which play an important role in the higher-dimensional enumerative geometry (gauge theory/calibrated submanifolds) approach to defining deformation invariants of G2G2-metrics. By varying the semi-Fanos used to build different G2G2-metrics on the same 77-manifold we can change the number of rigid associative 33-folds we produce.
Issue Date: 15-Jul-2015
Date of Acceptance: 13-Aug-2014
URI: http://hdl.handle.net/10044/1/30507
DOI: 10.1215/00127094-3120743
ISSN: 0012-7094
Publisher: Duke University Press
Start Page: 1971
End Page: 2092
Journal / Book Title: Duke Mathematical Journal
Volume: 164
Issue: 10
Copyright Statement: © 2015 Project Euclid
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/L001527/1
EP/G007241/1
EP/G06170X/1
EP/I008128/1
Keywords: Science & Technology
Physical Sciences
Mathematics
CALABI-YAU 3-FOLDS
CLASSIFICATION
DEFORMATIONS
MANIFOLDS
DESINGULARIZATIONS
SPACES
math.DG
math.DG
hep-th
math.AG
53C29, 53C38 (Primary) 53C25, 14J28, 14J30, 14J32, 14J45 (Secondary)
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Online Publication Date: 2015-07-14
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences