Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and
  Khovanov homology   This paper is an extended account of my "Introductory Plenary talk at Knots
in Hellas 2016" conference We start from the short introduction to Knot Theory
from the historical perspective, starting from Heraclas text (the first century
AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of
Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We
spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram
colorings (1956). In the second section we describe how Fox work was
generalized to distributive colorings (racks and quandles) and eventually in
the work of Jones and Turaev to link invariants via Yang-Baxter operators, here
the importance of statistical mechanics to topology will be mentioned. Finally
we describe recent developments which started with Mikhail Khovanov work on
categorification of the Jones polynomial. By analogy to Khovanov homology we
build homology of distributive structures (including homology of Fox colorings)
and generalize it to homology of Yang-Baxter operators. We speculate, with
supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter
homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of
pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants
of links) will be discussed and expanded.
  Dedicated to Lou Kauffman for his 70th birthday.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: q-bio