Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary

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).

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper25.abs.html

References in corpus (1)

• 2-Ruled Calibrated 4-folds in R^7 and R^8

Cited by in corpus (3)

• Asymptotically cylindrical 7-manifolds of holonomy G_2 with applications to compact irreducible G_2-manifolds
• Deformations of calibrated subbundles of Euclidean spaces via twisting by special sections
• McLean's second variation formula revisited