On a bounded runtime algorithm for the homeomorphism problem for hyperbolic manifolds
<p>We give a bounded runtime solution to the homeomorphism problem for closed hyperbolic 3-manifolds. This is an algorithm which, given two triangulations of hyperbolic 3-manifolds by at most t tetrahedra, decides if they represent the same hyperbolic 3-manifold with runtime bounded by 2²tO(t)...
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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2022
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| _version_ | 1826309216969687040 |
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| author | Scull, J |
| author2 | Lackenby, M |
| author_facet | Lackenby, M Scull, J |
| author_sort | Scull, J |
| collection | OXFORD |
| description | <p>We give a bounded runtime solution to the homeomorphism problem for closed hyperbolic 3-manifolds. This is an algorithm which, given two triangulations of hyperbolic 3-manifolds by at most t tetrahedra, decides if they represent the same hyperbolic 3-manifold with runtime bounded by 2²tO(t).</p>
<p>Along the way we prove two supplementary results, both of which we also prove in higher dimensions. First, we prove that one can compare geometric triangulations of hyperbolic n-manifolds in time bounded by 2²tO(nt³), n≥ 4, 2²tO(t), n = 3.</p>
<p>Second, we show that the length R of a systole of a closed or finite hyperbolic n-manifold (n ≥ 3) admitting a triangulation by t n-simplices can be bounded below by a function of n and t, namely R ≥ 1/ 2(nt)o(n⁴t).</p> |
| first_indexed | 2024-03-07T07:30:49Z |
| format | Thesis |
| id | oxford-uuid:b246c61b-e889-492e-ba67-ca2cc1e6983e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:30:49Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | oxford-uuid:b246c61b-e889-492e-ba67-ca2cc1e6983e2023-01-13T10:47:58ZOn a bounded runtime algorithm for the homeomorphism problem for hyperbolic manifoldsThesishttp://purl.org/coar/resource_type/c_db06uuid:b246c61b-e889-492e-ba67-ca2cc1e6983eEnglishHyrax Deposit2022Scull, JLackenby, MBridson, M<p>We give a bounded runtime solution to the homeomorphism problem for closed hyperbolic 3-manifolds. This is an algorithm which, given two triangulations of hyperbolic 3-manifolds by at most t tetrahedra, decides if they represent the same hyperbolic 3-manifold with runtime bounded by 2²tO(t).</p> <p>Along the way we prove two supplementary results, both of which we also prove in higher dimensions. First, we prove that one can compare geometric triangulations of hyperbolic n-manifolds in time bounded by 2²tO(nt³), n≥ 4, 2²tO(t), n = 3.</p> <p>Second, we show that the length R of a systole of a closed or finite hyperbolic n-manifold (n ≥ 3) admitting a triangulation by t n-simplices can be bounded below by a function of n and t, namely R ≥ 1/ 2(nt)o(n⁴t).</p> |
| spellingShingle | Scull, J On a bounded runtime algorithm for the homeomorphism problem for hyperbolic manifolds |
| title | On a bounded runtime algorithm for the homeomorphism problem for hyperbolic manifolds |
| title_full | On a bounded runtime algorithm for the homeomorphism problem for hyperbolic manifolds |
| title_fullStr | On a bounded runtime algorithm for the homeomorphism problem for hyperbolic manifolds |
| title_full_unstemmed | On a bounded runtime algorithm for the homeomorphism problem for hyperbolic manifolds |
| title_short | On a bounded runtime algorithm for the homeomorphism problem for hyperbolic manifolds |
| title_sort | on a bounded runtime algorithm for the homeomorphism problem for hyperbolic manifolds |
| work_keys_str_mv | AT scullj onaboundedruntimealgorithmforthehomeomorphismproblemforhyperbolicmanifolds |