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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.06132 |
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| _version_ | 1866908523724537856 |
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| author | Wang, Peng Zhang, Qiang Zhao, Xuezhi |
| author_facet | Wang, Peng Zhang, Qiang Zhao, Xuezhi |
| contents | 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 $M\times N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Jiang's Bounded Index Property for products of nilmanifolds Wang, Peng Zhang, Qiang Zhao, Xuezhi Geometric Topology Algebraic Topology 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 $M\times N$. |
| title | On Jiang's Bounded Index Property for products of nilmanifolds |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2507.06132 |