Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twisted duality for embedded graphs   We consider two operations on an edge of an embedded graph (or equivalently a
ribbon graph): giving a half-twist to the edge and taking the partial dual with
respect to the edge. These two operations give rise to an action of
S_3^{|E(G)|}, the ribbon group, on G. The action of the ribbon group on
embedded graphs extends the concepts of duality, partial duality and Petrie
duality. We show that this ribbon group action gives a complete
characterization of duality in that if G is any cellularly embedded graph with
medial graph G_m, then the orbit of G under the group action is precisely the
set of all graphs with medial graphs isomorphic (as abstract graphs) to G_m. We
provide characterizations of special sets of twisted duals, such as the partial
duals, of embedded graphs in terms of medial graphs and we show how different
kinds of graph isomorphism give rise to these various notions of duality. The
ribbon group action then leads to a deeper understanding of the properties of,
and relationships among, various graph polynomials via the generalized
transition polynomial which interacts naturally with the ribbon group action.

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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat