Quasifuchsian state surfaces

Futer, David; Kalfagianni, Efstratia; Purcell, Jessica

doi:10.1090/S0002-9947-2014-06182-5

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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