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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| Accès en ligne: | https://arxiv.org/abs/2102.11459 |
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| _version_ | 1866911114170728448 |
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| author | Piterman, Kevin Ivan Costa, Iván Sadofschi |
| author_facet | Piterman, Kevin Ivan Costa, Iván Sadofschi |
| contents | In this second part we prove that, if $G$ is one of the groups $\mathrm{PSL}_2(q)$ with $q>5$ and $q\equiv 5\pmod {24}$ or $q\equiv 13 \pmod{24}$, then the fundamental group of every acyclic $2$-dimensional, fixed point free and finite $G$-complex admits a nontrivial representation in a unitary group $\mathrm{U}(m)$. This completes the proof of the following result: every action of a finite group on a finite and contractible $2$-complex has a fixed point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_11459 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Group actions on contractible $2$-complexes II Piterman, Kevin Ivan Costa, Iván Sadofschi Algebraic Topology Group Theory Representation Theory 57M60 In this second part we prove that, if $G$ is one of the groups $\mathrm{PSL}_2(q)$ with $q>5$ and $q\equiv 5\pmod {24}$ or $q\equiv 13 \pmod{24}$, then the fundamental group of every acyclic $2$-dimensional, fixed point free and finite $G$-complex admits a nontrivial representation in a unitary group $\mathrm{U}(m)$. This completes the proof of the following result: every action of a finite group on a finite and contractible $2$-complex has a fixed point. |
| title | Group actions on contractible $2$-complexes II |
| topic | Algebraic Topology Group Theory Representation Theory 57M60 |
| url | https://arxiv.org/abs/2102.11459 |