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arXiv · 2507.06132

On Jiang's Bounded Index Property for products of nilmanifolds

Peng Wang·Qiang Zhang·Xuezhi Zhao
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Abstract

In 2023, Zhang and Zhao presented the first examples of aspherical manifolds lacking the Bounded Index Property (BIP) for fixed points. This answered a question posed by Jiang in 1998 in the negative. In this paper, we first extend the notion of BIP to that of iterates of selfmaps (BIP$_k$), and then demonstrate BIP$_k$ for certain products $M\times N$ of nilmanifolds. Finally, we give characterizations for the Lefschetz number, the Nielsen number, and the minimal number of fixed points of self-homotopy equivalences of $M\times N$.

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Peng Wang, Qiang Zhang, Xuezhi Zhao. 2025-09-08. On Jiang's Bounded Index Property for products of nilmanifolds. https://arxiv.org/abs/2507.06132

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