Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary

Joyce, Dominic¹ ; Salur, Sema²

¹ Lincoln College, University of Oxford, Oxford, OX1 3DR, United Kingdom
² Department of Mathematics, Northwestern University, Illinois 60208, USA

Geometry & topology, Tome 9 (2005) no. 2, pp. 1115-1146.

Résumé

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 $H^2\left(C,ℝ\right)$.

Détail

DOI : 10.2140/gt.2005.9.1115

Keywords: calibrated geometries, asymptotically cylindrical manifolds, $G_2$–manifolds, coassociative submanifolds, elliptic operators.

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