Geometry & Topology 9 (2005) 1115–1146

DOI: 10.2140/gt.2005.9.1115

arXiv: math.DG/0408137

Abstract

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 H²_cs(C,R) in H²(C,R).

Keywords

calibrated geometries, asymptotically cylindrical manifolds, G₂–manifolds, coassociative submanifolds, elliptic operators.

Mathematical Subject Classification

Primary: 53C15, 53C21, 53C38

Secondary: 58J05

References

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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

Authors