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Guts of Surfaces and the Colored Jones Polynomial

This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of...

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Main Authors: Futer, David. (Author, http://id.loc.gov/vocabulary/relators/aut), Kalfagianni, Efstratia. (http://id.loc.gov/vocabulary/relators/aut), Purcell, Jessica. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
Edition:1st ed. 2013.
Series:Lecture Notes in Mathematics, 2069
Subjects:
Manifolds (Mathematics).
Complex manifolds.
Hyperbolic geometry.
Manifolds and Cell Complexes (incl. Diff.Topology).
Hyperbolic Geometry.
Online Access:https://doi.org/10.1007/978-3-642-33302-6
Table of Contents:
  • 1 Introduction
  • 2 Decomposition into 3–balls
  • 3 Ideal Polyhedra
  • 4 I–bundles and essential product disks
  • 5 Guts and fibers
  • 6 Recognizing essential product disks
  • 7 Diagrams without non-prime arcs
  • 8 Montesinos links
  • 9 Applications
  • 10 Discussion and questions.

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