Volume 9, issue 2 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary

Dominic Joyce and Sema Salur

Geometry & Topology 9 (2005) 1115–1146

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 b+2(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 Hcs2(C, ) in H2(C, ).

Keywords
calibrated geometries, asymptotically cylindrical manifolds, $G_2$–manifolds, coassociative submanifolds, elliptic operators.
Mathematical Subject Classification 2000
Primary: 53C38, 53C15, 53C21
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
Authors
Dominic Joyce
Lincoln College
University of Oxford
Oxford
OX1 3DR
United Kingdom
Sema Salur
Department of Mathematics
Northwestern University
Illinois 60208
USA