Profinite almost rigidity in 3-manifolds
| Autor: | Xu, Xiaoyu |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove that any compact, orientable 3-manifold with empty or incompressible toral boundary is profinitely almost rigid among all compact, orientable, boundary-incompressible 3-manifolds, i.e. the profinite completion of its fundamental group determines its homeomorphism type up to finitely many possibilities. Moreover, the profinite completion of the fundamental group of a mixed 3-manifold, together with the peripheral structure, uniquely determines the homeomorphism type of its Seifert part (i.e. the maximal graph manifold components in the JSJ-decomposition). On the other hand, without assigning the peripheral structure, the profinite completion of a mixed 3- manifold group may not even determine the fundamental group of its Seifert part. The proof is based on JSJ-decomposition. Comment: 50 pages, comments are welcome! |
| Databáze: | arXiv |
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