Geometry & Topology, Vol. 9 (2005) Paper no. 25, pages 1115--1146.

Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary

Dominic Joyce, Sema Salur

Abstract. McLean proved that the moduli space of coassociative deformations of a compact coassociative 4-submanifold C in a G_2-manifold (M,phi,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 G_2-manifold (M,phi,g) is also a smooth manifold. Its dimension is the dimension of the positive subspace of the image of H^2_cs(C,R) in H^2(C,R).

Keywords. Calibrated geometries, asymptotically cylindrical manifolds, G_2-manifolds, coassociative submanifolds, elliptic operators.

AMS subject classification. Primary: 53C38, 53C15, 53C21. Secondary: 58J05.

DOI: 10.2140/gt.2005.9.1115

E-print: arXiv:math.DG/0408137

Submitted to GT on 12 August 2004. Paper accepted 7 May 2005. Paper published 1 June 2005.

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Dominic Joyce, Sema Salur
Lincoln College, Oxford, OX1 3DR, UK
Department of Mathematics, Northwestern University, IL 60208, USA

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