A Combinatorial Study of the Fixed Point Index
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916768976470016 |
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| author | López, Jesús A. Álvarez Majadas-Moure, Alejandro O. Mosquera-Lois, David |
| author_facet | López, Jesús A. Álvarez Majadas-Moure, Alejandro O. Mosquera-Lois, David |
| contents | We introduce a theory of integration with respect to the fixed point index, offering a substantial improvement over previous approaches based on the Lefschetz number. This framework eliminates several restrictive assumptions -- such as the need for definability, openness, or f-invariance of subspaces -- thereby allowing broader applicability. We also present a natural combinatorial adaptation of the fixed point index that extends the combinatorial Lefschetz number. This extension yields new topological and homotopical invariance results and facilitates the integration of real-valued functions with respect to fixed points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Combinatorial Study of the Fixed Point Index López, Jesús A. Álvarez Majadas-Moure, Alejandro O. Mosquera-Lois, David Algebraic Topology We introduce a theory of integration with respect to the fixed point index, offering a substantial improvement over previous approaches based on the Lefschetz number. This framework eliminates several restrictive assumptions -- such as the need for definability, openness, or f-invariance of subspaces -- thereby allowing broader applicability. We also present a natural combinatorial adaptation of the fixed point index that extends the combinatorial Lefschetz number. This extension yields new topological and homotopical invariance results and facilitates the integration of real-valued functions with respect to fixed points. |
| title | A Combinatorial Study of the Fixed Point Index |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2505.24530 |