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Ends of negatively curved manifolds Avramidi, Grigori

Description

A theorem of Gromov says that a complete finite volume Rieman- nian manifold of bounded negative curvature is the interior of a compact manifold with boundary. If, in addition, the curvature is bounded away from zero then the boundary is an aspherical manifold with virtually nilpotent fundamental group. I will discuss examples showing this is no longer true if the curvature is allowed to approach zero. Then, I will explain a recent result showing that in dimension four the boundary is aspherical. This is joint work with Yunhui Wu and Tam Nguyen Phan.

Item Metadata

Title	Ends of negatively curved manifolds
Creator	Avramidi, Grigori
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2013-08-08
Description	A theorem of Gromov says that a complete finite volume Rieman- nian manifold of bounded negative curvature is the interior of a compact manifold with boundary. If, in addition, the curvature is bounded away from zero then the boundary is an aspherical manifold with virtually nilpotent fundamental group. I will discuss examples showing this is no longer true if the curvature is allowed to approach zero. Then, I will explain a recent result showing that in dimension four the boundary is aspherical. This is joint work with Yunhui Wu and Tam Nguyen Phan.
Extent	40 minutes
Subject	Mathematics; Differential geometry; Manifolds and cell complexes
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of Chicago
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	10.14288/1.0043483
URI	http://hdl.handle.net/2429/49431
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Graduate
Rights URI	http://creativecommons.org/licenses/by-nc-nd/2.5/ca/
Aggregated Source Repository	DSpace

Item Media

201308080955-Avramidi_lrv.mp4 -- 172.4MB

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Attribution-NonCommercial-NoDerivs 2.5 Canada