scholarly journals Functoriality of colored link homologies

2018 ◽  
Vol 117 (5) ◽  
pp. 996-1040 ◽  
Author(s):  
Michael Ehrig ◽  
Daniel Tubbenhauer ◽  
Paul Wedrich
Keyword(s):  
Colored Link

scholarly journals Categorification of the Colored Jones Polynomial and Rasmussen Invariant of Links

2008 ◽  
Vol 60 (6) ◽  
pp. 1240-1266 ◽  
Author(s):  
Anna Beliakova ◽  
Stephan Wehrli
Keyword(s):  
Jones Polynomial ◽  
Special Choice ◽  
Colored Jones Polynomial ◽  
Two Parameters ◽  
Colored Link

AbstractWe define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphismclasses 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.

scholarly journals Slopes of links and signature formulas

2021 ◽  
pp. 93-105
Author(s):  
Alex Degtyarev ◽  
Vincent Florens ◽  
Ana Lecuona
Keyword(s):  
Close Relation ◽  
The Other ◽  
Homology Sphere ◽  
Integral Homology ◽  
Content Type ◽  
Univariate Case ◽  
Other Hand ◽  
The One ◽  
Colored Link ◽  
Signature Formula

We present a new invariant, called slope, of a colored link in an integral homology sphere and use this invariant to complete the signature formula for the splice of two links. We develop a number of ways of computing the slope and a few vanishing results. Besides, we discuss the concordance invariance of the slope and establish its close relation to the Conway polynomials, on the one hand, and to the Kojima–Yamasaki η \eta -function (in the univariate case) and Cochran invariants, on the other hand.

scholarly journals ON THE KAUFFMAN–VOGEL AND THE MURAKAMI–OHTSUKI–YAMADA GRAPH POLYNOMIALS

2012 ◽  
Vol 21 (10) ◽  
pp. 1250098 ◽  
Author(s):  
HAO WU
Keyword(s):  
Simple Circuit ◽  
Graph Polynomials ◽  
Graph Polynomial ◽  
Link Homology ◽  
Kauffman Polynomial ◽  
Colored Link

This paper consists of three parts. First, we generalize the Jaeger Formula to express the Kauffman–Vogel graph polynomial as a state sum of the Murakami–Ohtsuki–Yamada graph polynomial. Then, we demonstrate that reversing the orientation and the color of a MOY graph along a simple circuit does not change the 𝔰𝔩(N) Murakami–Ohtsuki–Yamada polynomial or the 𝔰𝔩(N) homology of this MOY graph. In fact, reversing the orientation and the color of a component of a colored link only changes the 𝔰𝔩(N) homology by an overall grading shift. Finally, as an application of the first two parts, we prove that the 𝔰𝔬(6) Kauffman polynomial is equal to the 2-colored 𝔰𝔩(4) Reshetikhin–Turaev link polynomial, which implies that the 2-colored 𝔰𝔩(4) link homology categorifies the 𝔰𝔬(6) Kauffman polynomial.

scholarly journals Topological imitation of a colored link with the same Dehn surgery manifold

2005 ◽  
Vol 146-147 ◽  
pp. 67-82 ◽  
Author(s):  
Akio Kawauchi
Keyword(s):  
Dehn Surgery ◽  
Colored Link
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