{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/140367"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/140367","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Lipschitz homotopies of mappings from 3-sphere to 2-sphere","abstract":"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).","abstract_html":"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).","abstract_has_math":false,"creators":["Berdnikov, Aleksandr"],"institution":"Massachusetts Institute of Technology","degree_name":"Doctoral","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mathematics","school":null,"contributors":[],"advisors":["Guth, Larry"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-06","date_published":"2021-06","updated_at":"2026-07-22T22:22:23Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"rights_urls":["http://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/140367","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Guth, Larry"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Department of Mathematics"]},{"key":"dc:creator","label":"Author","values":["Berdnikov, Aleksandr"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-02-15T17:02:31Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-02-15T17:02:31Z"]},{"key":"dc:date.issued","label":"Date","values":["2021-06"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctoral","Doctor of Philosophy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright - Educational Use Permitted","Copyright MIT"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/page/InC-EDU/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1721.1/140367"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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)."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Lipschitz homotopies of mappings from 3-sphere to 2-sphere"]}]}],"canonical_facts":{"dc:contributor.advisor":["Guth, Larry"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Mathematics"],"dc:creator":["Berdnikov, Aleksandr"],"dc:date.accessioned":["2022-02-15T17:02:31Z"],"dc:date.available":["2022-02-15T17:02:31Z"],"dc:date.issued":["2021-06"],"dc:description.abstract":["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)."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/140367"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"dc:rights.uri":["http://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Lipschitz homotopies of mappings from 3-sphere to 2-sphere"],"dc:type":["Thesis"],"thesis:degree_name":["Doctoral","Doctor of Philosophy"]},"updated_at":"2026-07-22T22:22:23Z"}