Iwip endomorphisms of free groups and fixed points of graph selfmaps
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913932759793664 |
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| author | Wang, Peng Zhang, Qiang |
| author_facet | Wang, Peng Zhang, Qiang |
| contents | In a paper from 2011, Jiang, Wang and Zhang studied the fixed points and fixed subgroups of selfmaps on a connected finite graph or a connected compact hyperbolic surface $X$. In particular, for any selfmap $f: X\to X$, they proved that a certain quantity defined in terms of the characteristic $\chr(f, \F)$ and the index $\ind(f, \F)$ of a fixed point class $\F$ of $f$ is bounded below by $2χ(X)$, where $χ(X)$ is the Euler characteristic of $X$. In this paper, we give a sufficient condition for when equality holds and hence we partially answer a question of Jiang, by studying iwip outer endomorphisms of free groups acting on stable trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02924 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Iwip endomorphisms of free groups and fixed points of graph selfmaps Wang, Peng Zhang, Qiang Geometric Topology Group Theory In a paper from 2011, Jiang, Wang and Zhang studied the fixed points and fixed subgroups of selfmaps on a connected finite graph or a connected compact hyperbolic surface $X$. In particular, for any selfmap $f: X\to X$, they proved that a certain quantity defined in terms of the characteristic $\chr(f, \F)$ and the index $\ind(f, \F)$ of a fixed point class $\F$ of $f$ is bounded below by $2χ(X)$, where $χ(X)$ is the Euler characteristic of $X$. In this paper, we give a sufficient condition for when equality holds and hence we partially answer a question of Jiang, by studying iwip outer endomorphisms of free groups acting on stable trees. |
| title | Iwip endomorphisms of free groups and fixed points of graph selfmaps |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2303.02924 |