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.

Citations

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

Altmetrics

Downloads

52 downloads since deposited on 06 Feb 2009
20 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

[img]
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 2)
Size: 1MB
View at publisher
[img]
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 1)
Size: 240kB

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations