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2020 On the bounded index property for products of aspherical polyhedra
Qiang Zhang, Shengkui Ye
Topol. Methods Nonlinear Anal. 56(2): 419-432 (2020). DOI: 10.12775/TMNA.2019.116

Abstract

A compact polyhedron $X$ is said to have the Bounded Index Property for Homotopy Equivalences (BIPHE) if there is a finite bound $\mathcal{B}$ such that for any homotopy equivalence $f\colon X\rightarrow X$ 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 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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Qiang Zhang. Shengkui Ye. "On the bounded index property for products of aspherical polyhedra." Topol. Methods Nonlinear Anal. 56 (2) 419 - 432, 2020. https://doi.org/10.12775/TMNA.2019.116

Information

Published: 2020
First available in Project Euclid: 5 December 2020

Digital Object Identifier: 10.12775/TMNA.2019.116

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.56 • No. 2 • 2020
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