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G&T Monographs |
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Deformations of asymptotically cylindrical coassociative
submanifolds with fixed boundary
Dominic Joyce and Sema Salur
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Geometry & Topology 9 (2005)
1115–1146
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Abstract
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McLean proved that the moduli space of coassociative
deformations of a compact coassociative 4–submanifold C in
a G2–manifold (M,φ,g) is a smooth manifold of
dimension equal to b2+(C). In this paper, we show
that the moduli space of coassociative deformations of a noncompact,
asymptotically cylindrical coassociative 4–fold C in an
asymptotically cylindrical G2–manifold (M,φ,g)
is also a smooth manifold. Its dimension is the dimension of the
positive subspace of the image of H2cs(C,R)
in H2(C,R).
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Keywords
calibrated geometries, asymptotically
cylindrical manifolds, G2–manifolds,
coassociative submanifolds, elliptic operators.
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Mathematical Subject Classification
Primary: 53C15, 53C21, 53C38
Secondary: 58J05
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Publication
Received: 12 August 2004
Accepted: 7 May 2005
Published: 1 June 2005
Proposed: Rob Kirby
Seconded: Simon Donaldson, Gang Tian
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