Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Braid graphs in simply-laced triangle-free Coxeter systems are cubical
  graphs   Any two reduced expressions for the same Coxeter group element are related by
a sequence of commutation and braid moves. We say that two reduced expressions
are braid equivalent if they are related via a sequence of braid moves, and the
corresponding equivalence classes are called braid classes. Each braid class
can be encoded in terms of a braid graph in a natural way. In this paper, we
study the structure of braid graphs in simply-laced Coxeter systems. We prove
that every reduced expression has a unique factorization as a product of
so-called links, which in turn induces a decomposition of the braid graph into
a box product of the braid graphs for each link factor. When the Coxeter graph
has no three-cycles, we use the decomposition to prove that braid graphs are
cubical by constructing an embedding of the braid graph into a hypercube graph
whose image is an induced subgraph of the hypercube. For a special class of
links, called Fibonacci links, we prove that this embedding is an isometry from
the corresponding braid graph to a Fibonacci cube graph.

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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: cs