关于非球面多面体乘积的有界指数性质
On the bounded index property for products of aspherical polyhedra
摘要：
一个紧致多面体$X$被称为具有同伦等价的有界指数性质（BIPHE），如果存在一个有限界$\mathcal{B}$使得对于任何同伦等价$f:X\rightarrow X$和$f$的任何不动点类$\mathbf{F}$，指数$|\mathrm{ind}(f,\mathbf{F})|\leq \mathcal{B}$。本文考虑了紧致多面体的乘积，给出了它具有双凸性的几个充分条件。证明了具有负截面曲率的闭黎曼流形，特别是双曲流形的乘积具有BIPHE，从而肯定地回答了蒋伯驹提出的一个问题的一个特例.
英文摘要：
A compact polyhedron $X$ is said to have the Bounded Index Property for Homotopy Equivalence (BIPHE) if there is a finite bound $\mathcal{B}$ such that for any homotopy equivalence $f:X\rightarrow X$ and any fixed point class $\mathbf{F}$ of $f$, the index $|\mathrm{ind}(f,\mathbf{F})|\leq \mathcal{B}$. In this note, we consider the product of compact polyhedra, and give some sufficient conditions for it to have BIPHE. Moreover, we show that the products of closed Riemannian manifolds with negative sectional curvature, in particular hyperbolic manifolds, have BIPHE, which gives an affirmative answer to a special case of a question asked by Boju Jiang.
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