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 ...
Read More
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.
Read Less
Add this copy of Guts of Surfaces and the Colored Jones Polynomial to cart. $41.39, new condition, Sold by JUGGERNAUTZ rated 5.0 out of 5 stars, ships from East Grand Rapids, MI, UNITED STATES, published 2012 by Springer.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Brand NEW! Orders ship same or next business day w/ free tracking. Choose Expedited shipping for fastest (2-6 business day) delivery. Satisfaction Guaranteed!
Add this copy of Guts of Surfaces and the Colored Jones Polynomial to cart. $46.96, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2012 by Springer.
Add this copy of Guts of Surfaces and the Colored Jones Polynomial to cart. $74.20, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2012 by Springer.
