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arXiv · 1203.3637

Invertible Dirac operators and handle attachments on manifolds with boundary

Mattias Dahl·Nadine Große
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Abstract

For spin manifolds with boundary we consider Riemannian metrics which are product near the boundary and are such that the corresponding Dirac operator is invertible when half-infinite cylinders are attached at the boundary. The main result of this paper is that these properties of a metric can be preserved when the metric is extended over a handle of codimension at least two attached at the boundary. Applications of this result include the construction of non-isotopic metrics with invertible Dirac operator, and a concordance existence and classification theorem.

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Mattias Dahl, Nadine Große. 2014-03-24. Invertible Dirac operators and handle attachments on manifolds with boundary. https://doi.org/10.1142/s1793525314500137

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