Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From veering triangulations to link spaces and back again   This paper is the third in a sequence establishing a dictionary between the
combinatorics of veering triangulations equipped with appropriate filling
slopes, and the dynamics of pseudo-Anosov flows (without perfect fits) on
closed three-manifolds.
  Our motivation comes from the work of Agol and Gu\'eritaud. Agol introduced
veering triangulations of mapping tori as a tool for understanding the surgery
parents of pseudo-Anosov mapping tori. Gu\'eritaud gave a new construction of
veering triangulations of mapping tori using the orbit spaces of their
suspension flows. Generalizing this, Agol and Gu\'eritaud announced a method
that, given a closed manifold with a pseudo-Anosov flow (without perfect fits),
produces a veering triangulation equipped with filling slopes.
  In this paper we build, from a veering triangulation, a canonical circular
order on the cusps of the universal cover. Using this we build the veering
circle and the link space. These are the first entries in the promised
dictionary. The latter corresponds to the orbit space of a flow; the former
corresponds to Fenley's boundary at infinity of the orbit space.
  In the other direction, and using our previous work, we prove that the
veering triangulation is recovered (up to canonical isomorphism) from the
dynamics of the fundamental group acting on the link space. This is the first
step in proving that our dictionary gives a bijection between the two theories.

5
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: mtrl-th
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: chem-ph