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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.18339 |
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| _version_ | 1866908503394746368 |
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| author | Williams, Lucas |
| author_facet | Williams, Lucas |
| contents | We compare different periodic point invariants for families of maps parameterized over a compact manifold. Malkiewich and Ponto showed that, in the case of a single map, the Fuller trace is equivalent to the collection of Reidmeister traces of iterates. In this paper, we show that, in contrast to the case of a single map, the fiberwise Fuller trace is a strictly more sensitive invariant than the collection of fiberwise Reidemeister traces of iterates. This resolves a conjecture of Malkiewich and Ponto. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18339 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparing Periodic Point Invariants for Parameterized Families of Maps Williams, Lucas Algebraic Topology Dynamical Systems 55M20, 57R19, 57R91, 55N22 We compare different periodic point invariants for families of maps parameterized over a compact manifold. Malkiewich and Ponto showed that, in the case of a single map, the Fuller trace is equivalent to the collection of Reidmeister traces of iterates. In this paper, we show that, in contrast to the case of a single map, the fiberwise Fuller trace is a strictly more sensitive invariant than the collection of fiberwise Reidemeister traces of iterates. This resolves a conjecture of Malkiewich and Ponto. |
| title | Comparing Periodic Point Invariants for Parameterized Families of Maps |
| topic | Algebraic Topology Dynamical Systems 55M20, 57R19, 57R91, 55N22 |
| url | https://arxiv.org/abs/2508.18339 |