English

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

Operator Algebras 2020-12-17 v1

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 L2L^2-index and prove a relative L2L^2-index theorem which is a relative version of Atiyah's L2L^2-index theorem.

Keywords

Cite

@article{arxiv.2012.09076,
  title  = {Relative Equivariant Coarse Index Theorem and Relative $L^2$-Index Theorem},
  author = {Xiaoman Chen and Yanlin Liu and Dapeng Zhou},
  journal= {arXiv preprint arXiv:2012.09076},
  year   = {2020}
}