论文标题
签名操作员的ROE指数的均匀同拷贝不变性
Uniform homotopy invariance of Roe Index of the signature operator
论文作者
论文摘要
在本文中，我们研究了有界几何形状的歧管签名操作员的ROE指数。我们的主要结果是证明该指数均匀的同质副本不变性。换句话说，我们表明，考虑到一个定向统一的统一均匀同托$ f ：（ m，g）\ longrightarrow（n，h）$之间的两个有界几何学的定向流形之间，我们有$ f_ \ star（ind_ {roe} d_m）= ind_m）= ind_ {ind_ {roe}（roe}（d_n）$。此外，我们还表明，同一结果考虑到Isometries以$ m $和$ n $作用的组$γ$，并假设$ f $ $ f $是$γ$ equivariant。 $γ$的作用的唯一假设是，这些商再次是有限几何形状的多种多样。
In this paper we study the Roe index of the signature operator of manifolds of bounded geometry. Our main result is the proof of the uniform homotopy invariance of this index. In other words we show that, given an orientation-preserving uniform homotopy equivalence $f:(M,g) \longrightarrow (N,h)$ between two oriented manifolds of bounded geometry, we have that $f_\star(Ind_{Roe}D_M) = Ind_{Roe}(D_N)$. Moreover we also show that the same result holds considering a group $Γ$ acting on $M$ and $N$ by isometries and assuming that $f$ is $Γ$-equivariant. The only assumption on the action of $Γ$ is that the quotients are again manifolds of bounded geometry.
