Contractibility of the orbit space of a saturated fusion system after Steinberg
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913547868438528 |
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| author | Dennaoui, Omar Villareal, Jonathon |
| author_facet | Dennaoui, Omar Villareal, Jonathon |
| contents | Recently, Steinberg used discrete Morse theory to give a new proof of a theorem of Symonds that the orbit space of the poset of nontrivial $p$-subgroups of a finite group is contractible. We extend Steinberg's argument in two ways, covering more general versions of the theorem that were already known. In particular, following a strategy of Libman, we give a discrete Morse theoretic argument for the contractibility of the orbit space of a saturated fusion system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00531 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Contractibility of the orbit space of a saturated fusion system after Steinberg Dennaoui, Omar Villareal, Jonathon Group Theory Combinatorics Recently, Steinberg used discrete Morse theory to give a new proof of a theorem of Symonds that the orbit space of the poset of nontrivial $p$-subgroups of a finite group is contractible. We extend Steinberg's argument in two ways, covering more general versions of the theorem that were already known. In particular, following a strategy of Libman, we give a discrete Morse theoretic argument for the contractibility of the orbit space of a saturated fusion system. |
| title | Contractibility of the orbit space of a saturated fusion system after Steinberg |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2401.00531 |