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arXiv · 1506.00110

Deformations of Asymptotically Cylindrical Cayley Submanifolds

Matthias Ohst
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Abstract

We study the deformations of an asymptotically cylindrical Cayley submanifold inside an asymptotically cylindrical Spin(7)-manifold. We prove an index formula for the operator of Dirac type that arises as the linearisation of the deformation map and show that if the Spin(7)-structure is generic, then there are no obstructions, and hence the moduli space is a smooth finite-dimensional manifold whose dimension is equal to the index of the operator of Dirac type. We further construct examples of asymptotically cylindrical Cayley submanifolds inside the asymptotically cylindrical Riemannian 8-manifolds with holonomy Spin(7) constructed by Kovalev.

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Matthias Ohst. 2015-05-30. Deformations of Asymptotically Cylindrical Cayley Submanifolds. https://arxiv.org/abs/1506.00110

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