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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Quasifuchsian state surfaces


Authors: David Futer, Efstratia Kalfagianni and Jessica S. Purcell
Journal: Trans. Amer. Math. Soc. 366 (2014), 4323-4343
MSC (2010): Primary 57M50, 57M27, 57M25; Secondary 20H10
Published electronically: April 22, 2014
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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
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
Email: jpurcell@math.byu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06182-5
PII: S 0002-9947(2014)06182-5
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.
Article copyright: © Copyright 2014 by the authors