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Optimal homotopies of curves on surfaces Chambers, Greg 2013-08-06
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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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https://iiif.library.ubc.ca/presentation/dsp.48630.1-0043479/manifest