Slopes and colored Jones polynomials of adequate knots

David Futer, Efstratia Kalfagianni, Jessica S. Purcell

Type: Article

Publication Date: 2010-12-29

Citations: 46

DOI: https://doi.org/10.1090/s0002-9939-2010-10617-2

Abstract

Garoufalidis conjectured a relation between the boundary slopes of a knot and its colored Jones polynomials. According to the conjecture, certain boundary slopes are detected by the sequence of degrees of the colored Jones polynomials. We verify this conjecture for adequate knots, a class that vastly generalizes that of alternating knots.

Locations

Proceedings of the American Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	A Jones slopes characterization of adequate knots	2016	Efstratia Kalfagianni
+ PDF Chat	A Jones slopes characterization of adequate knots	2018	Efstratia Kalfagianni
+	A Jones slopes characterization of adequate knots	2016	Efstratia Kalfagianni
+ PDF Chat	Remarks on Jones Slopes and Surfaces of Knots	2021	Efstratia Kalfagianni
+	Remarks on Jones slopes and surfaces of knots	2020	Efstratia Kalfagianni
+	Remarks on Jones slopes and surfaces of knots	2020	Efstratia Kalfagianni
+	Knot Cabling and the Degree of the Colored Jones Polynomial	2015	Efstratia Kalfagianni Anh T. Tran
+	Knot Cabling and the Degree of the Colored Jones Polynomial	2015	Efstratia Kalfagianni Anh Tran
+	Knot Cabling and the Degree of the Colored Jones Polynomial	2015	Efstratia Kalfagianni Anh T. Tran
+	The Jones polynomial and boundary slopes of alternating knots	2009	Cynthia L. Curtis S. J. Taylor
+ PDF Chat	THE JONES POLYNOMIAL AND BOUNDARY SLOPES OF ALTERNATING KNOTS	2011	Cynthia L. Curtis S. J. Taylor
+	The Jones polynomial and boundary slopes of alternating knots	2009	Cynthia L. Curtis S. J. Taylor
+	A characterization of adequate knots	2016	Efstratia Kalfagianni
+	A slope conjecture for links	2013	Roland van der Veen
+ PDF Chat	The slope conjecture for graph knots	2016	Kimihiko Motegi Toshie Takata
+	Cabling, connected sum operations and the slope conjecture	2015	Kimihiko Motegi Toshie Takata
+	The Slope Conjecture for a Family of Montesinos Knots	2017	Xudong Leng Zhiqing Yang Ximin Liu
+	The Slope Conjecture for 3-String Montesinos Knots	2018	Xudong Leng Zhiqing Yang Ximin Liu
+	Guts of surfaces and the colored Jones polynomial	2011	David Futer Efstratia Kalfagianni Jessica S. Purcell
+ PDF Chat	The slope conjecture for Montesinos knots	2020	Stavros Garoufalidis Christine Ruey Shan Lee Roland van der Veen

Works That Cite This (45)

Action	Title	Year	Authors
+	Repeated boundary slopes for 2-bridge knots	2015	Cynthia L. Curtis William Franczak Randolph J. Leiser Ryan J. Manheimer
+	Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3–manifolds	2020	Alex Casella Charles Katerba Stephan Tillmann
+	The strong slope conjecture for cablings and connected sums	2018	Kenneth L. Baker Kimihiko Motegi Toshie Takata
+	Quantum knot invariants	2018	Stavros Garoufalidis
+	The Slope Conjecture for Montesinos knots	2018	Stavros Garoufalidis Christine Ruey Shan Lee Roland van der Veen
+	Slopes for Pretzel Knots	2016	Christine Ruey Shan Lee Roland van der Veen
+	A slope conjecture for links	2015	Roland van der Veen
+ PDF Chat	The slope conjecture for Montesinos knots	2020	Stavros Garoufalidis Christine Ruey Shan Lee Roland van der Veen
+	A slope conjecture for links	2013	Roland van der Veen
+ PDF Chat	The strong slope conjecture and torus knots	2019	Efstratia Kalfagianni

Works Cited by This (15)

Action	Title	Year	Authors
+	Boundary Curves of Incompressible Surfaces	2004	Allen Hatcher
+ PDF Chat	Guts of Surfaces and the Colored Jones Polynomial	2012	David Futer Efstratia Kalfagianni Jessica S. Purcell
+ PDF Chat	On the boundary curves of incompressible surfaces	1982	Allen Hatcher
+ PDF Chat	THE JONES POLYNOMIAL AND BOUNDARY SLOPES OF ALTERNATING KNOTS	2011	Cynthia L. Curtis S. J. Taylor
+	A table of boundary slopes of Montesinos knots	2001	Nathan M. Dunfield
+	The Jones slopes of a knot	2009	Stavros Garoufalidis
+	Boundary slopes for Montesinos knots	1989	Allen Hatcher Ulrich Oertel
+	Some links with non-trivial polynomials and their crossing-numbers	1988	W. B. R. Lickorish Morwen Thistlethwaite
+	Essential state surfaces for knots and links	2006	Makoto Ozawa
+	The Jones polynomial and graphs on surfaces	2007	Oliver T. Dasbach David Futer Efstratia Kalfagianni Xiao-Song Lin Neal W. Stoltzfus