# Relative Equivariant Coarse Index Theorem and Relative $L^2$-Index Theorem

16 Dec 2020  ·  Xiaoman Chen, Yanlin Liu, Dapeng Zhou ·

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 $L^2$-index and prove a relative $L^2$-index theorem which is a relative version of Atiyah's $L^2$-index theorem.

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Operator Algebras