Guts of Surfaces and the Colored Jones Polynomial

Nonfiction, Science & Nature, Mathematics, Topology, Geometry
Cover of the book Guts of Surfaces and the Colored Jones Polynomial by David Futer, Efstratia Kalfagianni, Jessica Purcell, Springer Berlin Heidelberg
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: David Futer, Efstratia Kalfagianni, Jessica Purcell ISBN: 9783642333026
Publisher: Springer Berlin Heidelberg Publication: December 18, 2012
Imprint: Springer Language: English
Author: David Futer, Efstratia Kalfagianni, Jessica Purcell
ISBN: 9783642333026
Publisher: Springer Berlin Heidelberg
Publication: December 18, 2012
Imprint: Springer
Language: English

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 an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for the knot; in particular, the surface is a fiber if and only if a particular coefficient vanishes. We also relate hyperbolic volume to colored Jones polynomials. Our method is to generalize the checkerboard decompositions of alternating knots. Under mild diagrammatic hypotheses, we show that these surfaces are essential, and obtain an ideal polyhedral decomposition of their complement. We use normal surface theory to relate the pieces of the JSJ decomposition of the complement to the combinatorics of certain surface spines (state graphs). Since state graphs have previously appeared in the study of Jones polynomials, our method bridges the gap between quantum and geometric knot invariants.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for the knot; in particular, the surface is a fiber if and only if a particular coefficient vanishes. We also relate hyperbolic volume to colored Jones polynomials. Our method is to generalize the checkerboard decompositions of alternating knots. Under mild diagrammatic hypotheses, we show that these surfaces are essential, and obtain an ideal polyhedral decomposition of their complement. We use normal surface theory to relate the pieces of the JSJ decomposition of the complement to the combinatorics of certain surface spines (state graphs). Since state graphs have previously appeared in the study of Jones polynomials, our method bridges the gap between quantum and geometric knot invariants.

More books from Springer Berlin Heidelberg

Cover of the book Injuries and Health Problems in Football by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Experimental Methods in Hydraulic Research by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Handbuch Projektmanagement by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book The Northern North Atlantic by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book The Decade of Medicine or The Physician of the Rich and the Poor by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Learning Neuroimaging by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Quantum Dots for DNA Biosensing by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Infrastructure and Safety in a Collaborative World by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Autoimmune Pancreatitis by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Optimal Bundling by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Modern Techniques for Nano- and Microreactors/-reactions by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Construction and Reactivity of Pt-Based Bi-component Catalytic Systems by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Asymmetric Continuum by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Comparative Effectiveness and Efficacy Research and Analysis for Practice (CEERAP) by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Cellular Aspects of Hypertension by David Futer, Efstratia Kalfagianni, Jessica Purcell
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy