论文标题
相对模棱两可的粗索引定理和相对$ l^2 $ index定理
Relative Equivariant Coarse Index Theorem and Relative $L^2$-Index Theorem
论文作者
论文摘要
在本文中，我们给出了相对模棱两可的粗索引的定义，以适当的动作，并得出将该索引与局部eproivariant粗索引连接起来的相对模棱两可的粗索引定理。这是ROE在Arxiv中的相对粗索引定理的均等版本：Arch-Ever/1210.6100。此外，我们介绍了相对$ l^2 $ index的定义，并证明了相对$ l^2 $ index定理，该定理是Atiyah的$ l^2 $ index定理的相对版本。
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.
