Bismut–Cheeger Eta Form and Higher Spectral Flow
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Publication:6115182
DOI10.1093/IMRN/RNAC157arXiv2105.01926OpenAlexW4300705195MaRDI QIDQ6115182
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Publication date: 12 July 2023
Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)
Abstract: In this paper, using the equivariant version of the Dai-Zhang higher spectral flow, we generalize the variation formula, embedding formula and the adiabatic limit formula for the Atiyah-Patodi-Singer eta invariants to the equivariant Bismut-Cheeger eta forms for a fiberwise compact Lie group action when the kernels of corresponding fiberwise Dirac operators form equivariant vector bundles.
Full work available at URL: https://arxiv.org/abs/2105.01926
Index theory and related fixed-point theorems on manifolds (58J20) Invariance and symmetry properties for PDEs on manifolds (58J70) Eta-invariants, Chern-Simons invariants (58J28) Spectral flows (58J30)
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An extended variational formula for the Bismut-Cheeger eta form and its applications ⋮ The Bismut-Zhang embedding formula of APS reduced eta invariants: a simple and intrinsic geometrical proof
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