@prefix vivo: . @prefix edm: . @prefix dcterms: . @prefix dc: . @prefix skos: . @prefix ns0: . vivo:departmentOrSchool "Non UBC"@en ; edm:dataProvider "DSpace"@en ; dcterms:creator "Chambers, Greg"@en ; dcterms:issued "2014-08-06T23:55:03Z"@en, "2013-08-06"@en ; dcterms:description "In this talk, we will prove the following theorems. For any ǫ > 0, we have that:\\\\r\\\\n(1) If two simple closed curves on a 2-dimensional Riemannian manifold are homotopic through loops of length at most L, then they are also homotopic through simple closed curves of length at most L + ǫ (joint work with Y. Liokumovich).\\\\r\\\\n(2) If the boundary of a Riemannian 2-disc can be contracted through closed curves of length at most L, then it can be contracted through based loops of length at most L + 2D + ǫ, where D is the diameter of the 2-disc (joint work with R. Rotman). This result can be generalized for simple closed curves on Riemannian 2-manifolds.\\\\r\\\\n(3) A closed curve on an orientable Riemannian 2-manifold can be con- tracted through loops of length at most L + ǫ if the curve formed by traversing twice can be contracted through loops of length at most L (joint work with Y. Liokumovich). This can be seen as a quantitative version of the fact that the fundamental group of an orientable surface contains no elements of order 2."@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/49425?expand=metadata"@en ; dcterms:extent "51 minutes"@en ; dc:format "video/mp4"@en ; skos:note ""@en, "Author affiliation: University of Toronto"@en ; edm:isShownAt "10.14288/1.0043479"@en ; dcterms:language "eng"@en ; ns0:peerReviewStatus "Unreviewed"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ; dcterms:rights "Attribution-NonCommercial-NoDerivs 2.5 Canada"@en ; ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/2.5/ca/"@en ; ns0:scholarLevel "Graduate"@en ; dcterms:isPartOf "BIRS Workshop Lecture Videos (Banff, Alta)"@en ; dcterms:subject "Mathematics"@en, "Differential geometry"@en, "Manifolds and cell complexes"@en ; dcterms:title "Optimal homotopies of curves on surfaces"@en ; dcterms:type "Moving Image"@en ; ns0:identifierURI "http://hdl.handle.net/2429/49425"@en .