Title	Satellite operators and piecewise-linear concordance
Creator	Levine, Adam
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2016-02-26T11:16
Description	Every knot in the 3-sphere bounds a piecewise-linear (PL) disk in the 4-ball, but Akbulut showed in 1990 that the same is not true for knots in the boundary of an arbitrary contractible 4-manifold. We strengthen this result by showing that there exists a knot K in a homology sphere Y (which is the boundary of a contractible 4-manifold) such that K does not bound a PL disk in any homology 4-ball bounded by Y. The proof relies on using bordered Heegaard Floer homology to show that the action of a certain satellite operator on the knot concordance group is not surjective.
Extent	56 minutes
Subject	Mathematics; Manifolds and cell complexes; Differential geometry; Low dimensional topology
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Princeton University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2016-08-27
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0313304
URI	http://hdl.handle.net/2429/58998
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

Open Collections

BIRS Workshop Lecture Videos