Equivariant Trees and Partition Complexes
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914304154927104 |
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| author | Bergner, Julia E. Bonventre, Peter Calle, Maxine E. Chan, David Sarazola, Maru |
| author_facet | Bergner, Julia E. Bonventre, Peter Calle, Maxine E. Chan, David Sarazola, Maru |
| contents | We introduce two definitions of $G$-equivariant partitions of a finite $G$-set, both of which yield $G$-equivariant partition complexes. By considering suitable notions of equivariant trees, we show that $G$-equivariant partitions and $G$-trees are $G$-homotopy equivalent, generalizing existing results for the non-equivariant setting. Along the way, we develop equivariant versions of Quillen's Theorems A and B, which are of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08949 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equivariant Trees and Partition Complexes Bergner, Julia E. Bonventre, Peter Calle, Maxine E. Chan, David Sarazola, Maru Algebraic Topology Combinatorics Category Theory 55P91, 05A18, 20E08, 05E18 We introduce two definitions of $G$-equivariant partitions of a finite $G$-set, both of which yield $G$-equivariant partition complexes. By considering suitable notions of equivariant trees, we show that $G$-equivariant partitions and $G$-trees are $G$-homotopy equivalent, generalizing existing results for the non-equivariant setting. Along the way, we develop equivariant versions of Quillen's Theorems A and B, which are of independent interest. |
| title | Equivariant Trees and Partition Complexes |
| topic | Algebraic Topology Combinatorics Category Theory 55P91, 05A18, 20E08, 05E18 |
| url | https://arxiv.org/abs/2302.08949 |