Moduli spaces of 3-manifolds with boundary are finite
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Boyd, Rachael Bregman, Corey Steinebrunner, Jan |
| author_facet | Boyd, Rachael Bregman, Corey Steinebrunner, Jan |
| contents | We study the classifying space B Diff(M) of the diffeomorphism group of a connected, compact, orientable 3-manifold M. In the case that M is reducible we build a contractible space parametrising the systems of reducing spheres. We use this to prove that if M has non-empty boundary, then B Diff(M rel boundary) has the homotopy type of a finite CW complex. This was conjectured by Kontsevich and appears on the Kirby problem list as Problem 3.48. As a consequence, we are able to show that for every compact, orientable 3-manifold M, B Diff(M) has finite type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moduli spaces of 3-manifolds with boundary are finite Boyd, Rachael Bregman, Corey Steinebrunner, Jan Geometric Topology Algebraic Topology 57T20, 58D29 (primary), 57M50, 55R40, 57S05, 58D05 (secondary) We study the classifying space B Diff(M) of the diffeomorphism group of a connected, compact, orientable 3-manifold M. In the case that M is reducible we build a contractible space parametrising the systems of reducing spheres. We use this to prove that if M has non-empty boundary, then B Diff(M rel boundary) has the homotopy type of a finite CW complex. This was conjectured by Kontsevich and appears on the Kirby problem list as Problem 3.48. As a consequence, we are able to show that for every compact, orientable 3-manifold M, B Diff(M) has finite type. |
| title | Moduli spaces of 3-manifolds with boundary are finite |
| topic | Geometric Topology Algebraic Topology 57T20, 58D29 (primary), 57M50, 55R40, 57S05, 58D05 (secondary) |
| url | https://arxiv.org/abs/2404.12748 |