Volume 17, issue 3 (2017)

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

Volume 20
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

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
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
On bordered theories for Khovanov homology

Andrew Manion

Algebraic & Geometric Topology 17 (2017) 1557–1674
Abstract

We describe how to formulate Khovanov’s functor-valued invariant of tangles in the language of bordered Heegaard Floer homology. We then give an alternate construction of Lawrence Roberts’ type D and type A structures in Khovanov homology, and his algebra Γn, in terms of Khovanov’s theory of modules over the ring Hn. We reprove invariance and pairing properties of Roberts’ bordered modules in this language. Along the way, we obtain an explicit generators-and-relations description of Hn which may be of independent interest.

Keywords
Khovanov homology, bordered Floer homology, invariants of tangles, linear-quadratic algebras
Mathematical Subject Classification 2010
Primary: 57M27
References
Publication
Received: 12 November 2015
Revised: 13 July 2016
Accepted: 2 September 2016
Published: 17 July 2017
Authors
Andrew Manion
Department of Mathematics
UCLA
520 Portola Plaza
Los Angeles, CA 90095
United States
http://math.ucla.edu/~manion/