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Title	Optimal homotopies of curves on surfaces
Creator	Chambers, Greg
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2013-08-06
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.
Extent	51 minutes
Subject	Mathematics Differential geometry Manifolds and cell complexes
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: University of Toronto
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2014-08-06
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivs 2.5 Canada
DOI	10.14288/1.0043479
URI	http://hdl.handle.net/2429/49425
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Graduate
Rights URI	http://creativecommons.org/licenses/by-nc-nd/2.5/ca/
AggregatedSourceRepository	DSpace

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