Projective modules and the homotopy classification of $(G,n)$-complexes
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arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866910538140745728 |
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| author | Nicholson, John |
| author_facet | Nicholson, John |
| contents | A $(G,n)$-complex is an $n$-dimensional CW-complex with fundamental group $G$ and whose universal cover is $(n-1)$-connected. If $G$ has periodic cohomology then, for appropriate $n$, we show that there is a one-to-one correspondence between the homotopy types of finite $(G,n)$-complexes and the orbits of the stable class of a certain projective $\mathbb{Z} G$-module under the action of $\text{Aut}(G)$. We develop techniques to compute this action explicitly and use this to give an example where the action is non-trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_04252 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Projective modules and the homotopy classification of $(G,n)$-complexes Nicholson, John Algebraic Topology K-Theory and Homology A $(G,n)$-complex is an $n$-dimensional CW-complex with fundamental group $G$ and whose universal cover is $(n-1)$-connected. If $G$ has periodic cohomology then, for appropriate $n$, we show that there is a one-to-one correspondence between the homotopy types of finite $(G,n)$-complexes and the orbits of the stable class of a certain projective $\mathbb{Z} G$-module under the action of $\text{Aut}(G)$. We develop techniques to compute this action explicitly and use this to give an example where the action is non-trivial. |
| title | Projective modules and the homotopy classification of $(G,n)$-complexes |
| topic | Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2004.04252 |