Quasifuchsian state surfaces
Geometric Topology
2014-05-20 v2
Abstract
This paper continues our study, initiated in [arXiv:1108.3370], 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.
Cite
@article{arxiv.1209.5719,
title = {Quasifuchsian state surfaces},
author = {David Futer and Efstratia Kalfagianni and Jessica S. Purcell},
journal= {arXiv preprint arXiv:1209.5719},
year = {2014}
}
Comments
21 pages, 9 figures: To appear in the Transactions of the AMS