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Knot cobordisms, bridge index, and torsion in Floer homology

Abstract:

Given a connected cobordism between two knots in the 3‐sphere, our main result is an inequality involving torsion orders of the knot Floer homology of the knots, and the number of local maxima and the genus of the cobordism. This has several topological applications: The torsion order gives lower bounds on the bridge index and the band‐unlinking number of a knot, the fusion number of a ribbon knot, and the number of minima appearing in a slice disk of a knot. It also gives a lower bound on...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/topo.12170

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0003-3705-2288
Publisher:
Wiley Publisher's website
Journal:
Journal of Topology Journal website
Volume:
13
Issue:
4
Pages:
1701-1724
Publication date:
2020-10-26
Acceptance date:
2020-09-10
DOI:
EISSN:
1753-8424
ISSN:
1753-8416
Language:
English
Keywords:
Pubs id:
1131467
Local pid:
pubs:1131467
Deposit date:
2020-09-10

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