Volume 20, issue 6 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Concordance maps in knot Floer homology

András Juhász and Marco Marengon

Geometry & Topology 20 (2016) 3623–3673
Abstract

We show that a decorated knot concordance C from K to K induces a homomorphism FC on knot Floer homology that preserves the Alexander and Maslov gradings. Furthermore, it induces a morphism of the spectral sequences to HF̂(S3)2 that agrees with FC on the E1 page and is the identity on the E page. It follows that FC is nonvanishing on HFK̂0(K,τ(K)). We also obtain an invariant of slice disks in homology 4–balls bounding S3.

If C is invertible, then FC is injective, hence

dimHFK̂j(K,i) dimHFK̂j(K,i)

for every i,j . This implies an unpublished result of Ruberman that if there is an invertible concordance from the knot K to K, then g(K) g(K), where g denotes the Seifert genus. Furthermore, if g(K) = g(K) and K is fibred, then so is K.

Keywords
concordance, knot Floer homology, genus
Mathematical Subject Classification 2010
Primary: 57M27, 57R58
References
Publication
Received: 18 September 2015
Revised: 25 January 2016
Accepted: 24 February 2016
Published: 21 December 2016
Proposed: Ciprian Manolescu
Seconded: Peter Teichner, Ronald Stern
Authors
András Juhász
Mathematical Institute
University of Oxford
Andrew Wiles Building, Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
United Kingdom
http://www.maths.ox.ac.uk/people/andras.juhasz
Marco Marengon
Department of Mathematics
Imperial College London
180 Queen’s Gate
London
SW7 2AZ
United Kingdom
http://www.imperial.ac.uk/people/m.marengon13