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Guts of Surfaces and the Colored Jones Polynomial
Futer, David; Kalfagianni, Efstratia; Purcell, Jessica
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Description for Guts of Surfaces and the Colored Jones Polynomial
Paperback. The monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. This book proves that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. Series: Lecture Notes in Mathematics. Num Pages: 180 pages, 17 black & white illustrations, 45 colour illustrations, biography. BIC Classification: PBMS. Category: (P) Professional & Vocational. Dimension: 154 x 235 x 11. Weight in Grams: 290.
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 ... 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 ... Read more
Product Details
Format
Paperback
Publication date
2012
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Germany
Number of pages
220
Condition
New
Series
Lecture Notes in Mathematics
Number of Pages
170
Place of Publication
Berlin, Germany
ISBN
9783642333019
SKU
V9783642333019
Shipping Time
Usually ships in 15 to 20 working days
Ref
99-15
Reviews for Guts of Surfaces and the Colored Jones Polynomial
From the reviews: “A relationship between the geometry of knot complements and the colored Jones polynomial is given in this monograph. The writing is well organized and comprehensive, and the book is accessible to both researchers and graduate students with some background in geometric topology and Jones-type invariants.” (Heather A. Dye, Mathematical Reviews, January, 2014)