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Fibered faces, veering triangulations, and the arc complex

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Abstract

We study the connections between subsurface projections in curve and arc complexes in fibered 3-manifolds and Agol’s veering triangulation. The main theme is that large-distance subsurfaces in fibers are associated to large simplicial regions in the veering triangulation, and this correspondence holds uniformly for all fibers in a given fibered face of the Thurston norm.

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Authors and Affiliations

  1. Department of Mathematics, Yale University, 10 Hillhouse Ave., New Haven, CT, 06511, USA

    Yair N. Minsky

  2. Department of Mathematics, Temple University, 1805 North Broad Street, Philadelphia, PA, 19122, USA

    Samuel J. Taylor

Authors
  1. Yair N. Minsky
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  2. Samuel J. Taylor
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Correspondence to Samuel J. Taylor.

Additional information

This work was partially supported by NSF Grants DMS-1311844 and DMS-1400498.

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Minsky, Y.N., Taylor, S.J. Fibered faces, veering triangulations, and the arc complex. Geom. Funct. Anal. 27, 1450–1496 (2017). https://doi.org/10.1007/s00039-017-0430-y

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  • DOI: https://doi.org/10.1007/s00039-017-0430-y

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