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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2505.22376 |
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| _version_ | 1866915310161887232 |
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| author | Küçük, Başak |
| author_facet | Küçük, Başak |
| contents | Both the Klein-Williams invariant $\ell_G(f)$ from \cite{KW2} and the generalized equivariant Lefschetz invariant $λ_G(f)$ from \cite{weber07} serve as complete obstructions to the fixed point problem in the equivariant setting. The latter is functorial in the sense of Definition \ref{functorial}. The first part of this paper aims to demonstrate that $\ell_G(f)$ is also functorial. The second part summarizes the ``universality" theory of such functorial invariants, developed in \cites{lueck1999, Weber06}, and explicitly computes the group in which the universal invariant lies, under a certain hypothesis. The final part explores the relationship between $\ell_G(f)$ and $λ_G(f)$, and presents examples to compare $\ell_G(f)$, $λ_G(f)$, and the universal invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22376 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functoriality of the Klein-Williams Invariant and Universality Theory Küçük, Başak Algebraic Topology Both the Klein-Williams invariant $\ell_G(f)$ from \cite{KW2} and the generalized equivariant Lefschetz invariant $λ_G(f)$ from \cite{weber07} serve as complete obstructions to the fixed point problem in the equivariant setting. The latter is functorial in the sense of Definition \ref{functorial}. The first part of this paper aims to demonstrate that $\ell_G(f)$ is also functorial. The second part summarizes the ``universality" theory of such functorial invariants, developed in \cites{lueck1999, Weber06}, and explicitly computes the group in which the universal invariant lies, under a certain hypothesis. The final part explores the relationship between $\ell_G(f)$ and $λ_G(f)$, and presents examples to compare $\ell_G(f)$, $λ_G(f)$, and the universal invariant. |
| title | Functoriality of the Klein-Williams Invariant and Universality Theory |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2505.22376 |