#### Volume 9, issue 2 (2005)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear 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 ${G}_{2}$–manifold $\left(M,\phi ,g\right)$ is a smooth manifold of dimension equal to ${b}_{+}^{2}\left(C\right)$. 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 $\left(M,\phi ,g\right)$ is also a smooth manifold. Its dimension is the dimension of the positive subspace of the image of ${H}_{cs}^{2}\left(C,ℝ\right)$ in ${H}^{2}\left(C,ℝ\right)$.

##### Keywords
calibrated geometries, asymptotically cylindrical manifolds, $G_2$–manifolds, coassociative submanifolds, elliptic operators.
##### Mathematical Subject Classification 2000
Primary: 53C38, 53C15, 53C21
Secondary: 58J05
##### 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