On the finiteness of the classifying space of diffeomorphisms of reducible three manifolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866916710739607552 |
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| author | Nariman, Sam |
| author_facet | Nariman, Sam |
| contents | Kontsevich conjectured that $\text{BDiff}(M, \text{rel }\partial)$ has the homotopy type of a finite CW complex for all compact $3$-manifolds with non-empty boundary. Hatcher-McCullough proved this conjecture when $M$ is irreducible. We prove a homological version of Kontsevich's conjecture. More precisely, we show that $\text{BDiff}(M, \text{rel }\partial)$ has finitely many nonzero homology groups, each finitely generated, when $M$ is a connected sum of irreducible $3$-manifolds that each have a nontrivial and non-spherical boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_12338 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the finiteness of the classifying space of diffeomorphisms of reducible three manifolds Nariman, Sam Geometric Topology Algebraic Topology 57R50, 57R19, 57M60, 57M07, 55R40, 57S05, 58D05 Kontsevich conjectured that $\text{BDiff}(M, \text{rel }\partial)$ has the homotopy type of a finite CW complex for all compact $3$-manifolds with non-empty boundary. Hatcher-McCullough proved this conjecture when $M$ is irreducible. We prove a homological version of Kontsevich's conjecture. More precisely, we show that $\text{BDiff}(M, \text{rel }\partial)$ has finitely many nonzero homology groups, each finitely generated, when $M$ is a connected sum of irreducible $3$-manifolds that each have a nontrivial and non-spherical boundary. |
| title | On the finiteness of the classifying space of diffeomorphisms of reducible three manifolds |
| topic | Geometric Topology Algebraic Topology 57R50, 57R19, 57M60, 57M07, 55R40, 57S05, 58D05 |
| url | https://arxiv.org/abs/2104.12338 |