Volume 17, issue 5 (2017)

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

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Link homology and equivariant gauge theory

Prayat Poudel and Nikolai Saveliev

Algebraic & Geometric Topology 17 (2017) 2635–2685
Abstract

Singular instanton Floer homology was defined by Kronheimer and Mrowka in connection with their proof that Khovanov homology is an unknot detector. We study this theory for knots and two-component links using equivariant gauge theory on their double branched covers. We show that the special generator in the singular instanton Floer homology of a knot is graded by the knot signature mod 4, thereby providing a purely topological way of fixing the absolute grading in the theory. Our approach also results in explicit computations of the generators and gradings of the singular instanton Floer chain complex for several classes of knots with simple double branched covers, such as two-bridge knots, some torus knots, and Montesinos knots, as well as for several families of two-component links.

Keywords
Floer homology, equivariant gauge theory, knots, links, Khovanov homology
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57R58
References
Publication
Received: 15 June 2015
Accepted: 23 June 2017
Published: 19 September 2017
Authors
Prayat Poudel
Department of Mathematics & Statistics
McMaster University
Hamilton
ON
Canada
http://www.ms.mcmaster.ca/~ppoudel
Nikolai Saveliev
Department of Mathematics
University of Miami
Coral Gables
FL
United States
http://www.math.miami.edu/~saveliev