Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Step by step categorification of the Jones polynomial in Kauffman's
  version   Given any diagram of a link, we define on the cube of Kauffman's states a
"2-complex" whose homology is an invariant of the associated framed links, and
such that the graded Euler characteristic reproduces the unnormalized Kauffman
bracket. This includes a categorification of brackets skein relation. Then we
incorporate the orientation information and get a further complex on the same
cube that gives rise to a new invariant homology for oriented links, so that
the graded Euler characteristic reproduces the unnormalized Jones polynomial in
Kauffman's version. Finally we clarify the relations between this homology and
the original Khovanov homology of oriented links, extending the well known
relation between the associated two versions of the Jones polynomial.

14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: econ