Header

UZH-Logo

Maintenance Infos

Categorification of the colored Jones polynomial and Rasmussen invariant of links


Beliakova, A; Wehrli, S (2008). Categorification of the colored Jones polynomial and Rasmussen invariant of links. Canadian Journal of Mathematics, 60(6):1240-1266.

Abstract

We define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further, we study conditions under which framed colored link cobordisms induce chain transformations between our formal brackets. We conjecture that for special choice of parameters, Khovanov and Lee homology theories of colored links are functorial (up to sign). Finally, we extend the Rasmussen invariant to links and give examples where this invariant is a stronger obstruction to sliceness than the multivariable Levine–Tristram signature.

Abstract

We define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further, we study conditions under which framed colored link cobordisms induce chain transformations between our formal brackets. We conjecture that for special choice of parameters, Khovanov and Lee homology theories of colored links are functorial (up to sign). Finally, we extend the Rasmussen invariant to links and give examples where this invariant is a stronger obstruction to sliceness than the multivariable Levine–Tristram signature.

Statistics

Citations

19 citations in Web of Science®
14 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

60 downloads since deposited on 06 Feb 2009
8 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Khovanov homology, colored Jones polynomial, slice genus, movie moves, framed cobordism
Language:English
Date:2008
Deposited On:06 Feb 2009 08:17
Last Modified:05 Apr 2016 12:57
Publisher:University of Toronto Press
ISSN:0008-414X
Publisher DOI:https://doi.org/10.4153/CJM-2008-053-1
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2462446
http://arxiv.org/abs/math/0510382v2

Download

Download PDF  'Categorification of the colored Jones polynomial and Rasmussen invariant of links'.
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 2)
Size: 1MB
View at publisher
Download PDF  'Categorification of the colored Jones polynomial and Rasmussen invariant of links'.
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 1)
Size: 240kB