Relative Equivariant Coarse Index Theorem and Relative L²-Index Theorem

2020/12/16 by Xiaoman Chen, Yanlin Liu, Chen, Xiaoman +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.2012.09076

Abstract

In this paper, we give a definition of the relative equivariant coarse index for proper actions and derive a relative equivariant coarse index theorem connecting this index with the localized equivariant coarse indices. This is an equivariant version of Roe's relative coarse index theorem in arXiv:arch-ive/1210.6100. Furthermore, we present a definition of the relative L²-index and prove a relative L²-index theorem which is a relative version of Atiyah's L²-index theorem.

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