Document Type
Article
Date
8-18-2006
Disciplines
Mathematics
Description/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.
Recommended Citation
Beliakova, Anna and Wehrli, Stephan, "Categorification of the Colored Jones Polynomial and Rasmussen Invariant of Links" (2006). Mathematics - All Scholarship. 114.
https://surface.syr.edu/mat/114
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/math/0510382