Real embedding and equivariant eta forms

Liu, Bo

doi:10.1007/s00209-018-2119-9

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Real embedding and equivariant eta forms

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Liu, Bo
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00209-018-2119-9
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arXiv:1706.07121.pdf
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Liu, B. (2019). Real embedding and equivariant eta forms. Mathematische Zeitschrift, 292(3-4), 849-878. doi:10.1007/s00209-018-2119-9.

Cite as: https://hdl.handle.net/21.11116/0000-0004-9BD4-E

Abstract

Bismut and Zhang (Math Ann 295(4):661–684,
1993) establish a mod Z embedding formula
of Atiyah–Patodi–Singer reduced eta invariants. In this paper, we explain the hidden mod Z
term as a spectral flow and extend this embedding formula to the equivariant family case. In this case, the spectral flow is generalized to the equivariant Chern character of some equivariant Dai–Zhang higher spectral flow.