Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary

Details Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary

2004-08-10

arxiv.org/abs/math/0408137v2

Geom. Topol. 9(2005) 1115-1146

Mathematics

Differential Geometry

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

Scientific paper

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).

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