TY - JOUR
T1 - Quasifuchsian state surfaces
AU - Futer, David
AU - Kalfagianni, Efstratia
AU - Purcell, Jessica Shepherd
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
UR - http://www.ams.org/journals/tran/2014-366-08/S0002-9947-2014-06182-5/S0002-9947-2014-06182-5.pdf
U2 - 10.1090/S0002-9947-2014-06182-5
DO - 10.1090/S0002-9947-2014-06182-5
M3 - Article
VL - 366
SP - 4323
EP - 4343
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 8
ER -