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Search: MSC category 18G60 ( Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22] )

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1. CJM 2008 (vol 60 pp. 1240)

Beliakova, Anna; Wehrli, Stephan
Categorification of the Colored Jones Polynomial and Rasmussen Invariant of Links
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.

Keywords:Khovanov homology, colored Jones polynomial, slice genus, movie moves, framed cobordism
Categories:57M25, 57M27, 18G60

2. CJM 2000 (vol 52 pp. 1310)

Yagunov, Serge
On the Homology of $\GL_n$ and Higher Pre-Bloch Groups
For every integer $n>1$ and infinite field $F$ we construct a spectral sequence converging to the homology of $\GL_n(F)$ relative to the group of monomial matrices $\GM_n(F)$. Some entries in $E^2$-terms of these spectral sequences may be interpreted as a natural generalization of the Bloch group to higher dimensions. These groups may be characterized as homology of $\GL_n$ relatively to $\GL_{n-1}$ and $\GM_n$. We apply the machinery developed to the investigation of stabilization maps in homology of General Linear Groups.

Categories:19D55, 20J06, 18G60

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