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arxiv: math/0105160 · v1 · submitted 2001-05-18 · 🧮 math.DG · math.FA· math.SP

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Equivariant spectral flow and a Lefschetz theorem on odd dimensional spin manifolds

Hao Fang
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classification 🧮 math.DG math.FAmath.SP
keywords manifoldsequivariantlefschetzoperatorsspectralspintheoremconsequence
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A notion of equivariant spectral flows for families of self-dual elliptic operators on Riemannian manifolds is purposed. As a consequence, a local version of a Lefschetz fix point theorem is proved for Toeplitz operators on odd-dimensional spin manifolds.

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  1. Reflection Symmetry, APS Boundary Conditions, and Equivariant Spectral Flow on a Warped Cylinder

    math-ph 2026-05 unverdicted novelty 6.0

    Reflection symmetry on twisted Dirac operators on warped cylinders holds precisely when 2A is integer, yielding unitary equivalence of APS blocks and an RO(O(2))-valued or mod-two spectral-flow invariant.