Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A graphical calculus for tangles in surfaces   We show how the theory of tangles is equivalent to that of well-connected
tangles. These are drawn on a surface with boundary, and equivalent via
Reidemeister moves of a restricted kind. This reworking of the graphical
foundations for link and tangle theory can be expected to have a variety of
applications, including ones involving 3-manifolds. It opens the way to new
approaches for defining `facial' state-sum invariants that depend in part on
assigning substates to faces of tangle diagrams.

20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
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The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph