Homotopy equivalence of spaces of metrics with invertible Dirac operator

Nadine Große; Niccolò Pederzani

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arXiv · 1910.09167

Homotopy equivalence of spaces of metrics with invertible Dirac operator

Nadine Große·Niccolò Pederzani

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Abstract

We prove that for cobordant closed spin manifolds of dimension $n\geq 3$ the associated spaces of metrics with invertible Dirac operator are homotopy equivalent. This is the spinorial counterpart of a similar result on positive scalar curvature of Chernysh/Walsh and generalizes the surgery result of Ammann-Dahl-Humbert on the existence of metrics with invertible Dirac operator under surgery. We also give a relative statement of this homotopy equivalence.

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Nadine Große, Niccolò Pederzani. 2019-10-21. Homotopy equivalence of spaces of metrics with invertible Dirac operator. https://arxiv.org/abs/1910.09167

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