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 Hysteresis Phenomena in Biology by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Cartilage Lesions of the Ankle by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Applications of Chaos and Nonlinear Dynamics in Engineering - Vol. 1 by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Erfolgreich Starten ins Ingenieurstudium by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Honeybees of Asia by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Resuscitation and Life Support in Disasters, Relief of Pain and Suffering in Disaster Situations by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Terahertz Techniques by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book The Global Politics of Science and Technology - Vol. 1 by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Identitätsmanagement im Cloud Computing by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Study on Climate Change in Southwestern China by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Corporate Governance in Emerging Markets by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Models of Strategic Reasoning by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Metalation of Azines and Diazines by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book Endocrines and Osmoregulation by David Futer, Efstratia Kalfagianni, Jessica Purcell
Cover of the book New Molecular Mechanisms of Estrogen Action and Their Impact on Future Perspectives in Estrogen Therapy 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