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Proceedings of the London Mathematical Society Advance Access originally published online on March 3, 2009
Proceedings of the London Mathematical Society 2009 99(2):386-424; doi:10.1112/plms/pdp006
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© 2009 London Mathematical Society

Deformation theory of asymptotically conical coassociative 4-folds

Jason D. Lotay

University College
High Street
Oxford
OX1 4BH

Received 15 May 2007. Revision received 17 December 2008.

Suppose that a coassociative 4-fold N in R7 is asymptotically conical (AC) to a cone C with rate {lambda} < 1. If {lambda} isin [–2, 1) is generic, then we show that the moduli space of coassociative deformations of N that are also AC to C with rate {lambda} is a smooth manifold, and we calculate its dimension. If {lambda} < – 2 and generic, then we show that the moduli space is locally homeomorphic to the kernel of a smooth map between smooth manifolds, and we give a lower bound for its expected dimension. We also derive a test for when N will be planar if {lambda} < – 2 and we discuss examples of AC coassociative 4-folds.

2000 Mathematics Subject Classification 53C38.


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