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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Quasifuchsian state surfaces
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by David Futer, Efstratia Kalfagianni and Jessica S. Purcell PDF
Trans. Amer. Math. Soc. 366 (2014), 4323-4343

Abstract:

This paper continues our study of essential state surfaces in link complements that satisfy a mild diagrammatic hypothesis (homogeneously adequate). For hyperbolic links, we show that the geometric type of these surfaces in the Thurston trichotomy is completely determined by a simple graph–theoretic criterion in terms of a certain spine of the surfaces. For links with $A$– or $B$–adequate diagrams, the geometric type of the surface is also completely determined by a coefficient of the colored Jones polynomial of the link.
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Additional Information
  • David Futer
  • Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
  • MR Author ID: 671567
  • ORCID: 0000-0002-2595-6274
  • Email: dfuter@temple.edu
  • Efstratia Kalfagianni
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • Email: kalfagia@math.msu.edu
  • Jessica S. Purcell
  • Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
  • MR Author ID: 807518
  • ORCID: 0000-0002-0618-2840
  • Email: jpurcell@math.byu.edu
  • Received by editor(s): October 4, 2012
  • Published electronically: April 22, 2014
  • Additional Notes: The first author was supported in part by NSF grant DMS–1007221.
    The second author was supported in part by NSF grant DMS–1105843.
    The third author was supported in part by NSF grant DMS–1007437 and a Sloan Research Fellowship.
  • © Copyright 2014 by the authors
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 4323-4343
  • MSC (2010): Primary 57M50, 57M27, 57M25; Secondary 20H10
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06182-5
  • MathSciNet review: 3206461