Homotopy equivalence of spaces of metrics with invertible Dirac operator

2019/10/21 by Nadine Große, Große, Nadine, Pederzani, Niccolò · 1 citation
Mathematics · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1910.09167

openalex publication_date 2019/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for cobordant closed spin manifolds of dimension n≥ 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.

Citations

• On the homotopy type of the space R⁺(M)

Cited by

• The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4

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