Lipschitz homotopies of mappings from 3-sphere to 2-sphere
This work focuses on important step in quantitative topology: given homotopic mappings from S^m to S^n of Lipschitz constant L, build the (asymptotically) simplest homotopy between them (meaning having the least Lipschitz constant). The present paper resolves this problem for the first case where Ho...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2022
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| Online Access: | https://hdl.handle.net/1721.1/140367 |
| _version_ | 1826215524029169664 |
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| author | Berdnikov, Aleksandr |
| author2 | Guth, Larry |
| author_facet | Guth, Larry Berdnikov, Aleksandr |
| author_sort | Berdnikov, Aleksandr |
| collection | MIT |
| description | This work focuses on important step in quantitative topology: given homotopic mappings from S^m to S^n of Lipschitz constant L, build the (asymptotically) simplest homotopy between them (meaning having the least Lipschitz constant). The present paper resolves this problem for the first case where Hopf invariant plays a role: m = 3, n = 2, constructing a homotopy with Lipschitz constant O(L). |
| first_indexed | 2024-09-23T16:33:14Z |
| format | Thesis |
| id | mit-1721.1/140367 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:33:14Z |
| publishDate | 2022 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1403672022-02-16T03:01:53Z Lipschitz homotopies of mappings from 3-sphere to 2-sphere Berdnikov, Aleksandr Guth, Larry Massachusetts Institute of Technology. Department of Mathematics This work focuses on important step in quantitative topology: given homotopic mappings from S^m to S^n of Lipschitz constant L, build the (asymptotically) simplest homotopy between them (meaning having the least Lipschitz constant). The present paper resolves this problem for the first case where Hopf invariant plays a role: m = 3, n = 2, constructing a homotopy with Lipschitz constant O(L). Ph.D. 2022-02-15T17:02:31Z 2022-02-15T17:02:31Z 2021-06 2021-05-25T12:46:40.184Z Thesis https://hdl.handle.net/1721.1/140367 0000-0002-4709-7802 In Copyright - Educational Use Permitted Copyright MIT http://rightsstatements.org/page/InC-EDU/1.0/ application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Berdnikov, Aleksandr Lipschitz homotopies of mappings from 3-sphere to 2-sphere |
| title | Lipschitz homotopies of mappings from 3-sphere to 2-sphere |
| title_full | Lipschitz homotopies of mappings from 3-sphere to 2-sphere |
| title_fullStr | Lipschitz homotopies of mappings from 3-sphere to 2-sphere |
| title_full_unstemmed | Lipschitz homotopies of mappings from 3-sphere to 2-sphere |
| title_short | Lipschitz homotopies of mappings from 3-sphere to 2-sphere |
| title_sort | lipschitz homotopies of mappings from 3 sphere to 2 sphere |
| url | https://hdl.handle.net/1721.1/140367 |
| work_keys_str_mv | AT berdnikovaleksandr lipschitzhomotopiesofmappingsfrom3sphereto2sphere |