03418nam 2200625Ia 450 991043814380332120200520144314.03-642-33302-810.1007/978-3-642-33302-6(CKB)3400000000102777(SSID)ssj0000831484(PQKBManifestationID)11470845(PQKBTitleCode)TC0000831484(PQKBWorkID)10872882(PQKB)10283002(DE-He213)978-3-642-33302-6(MiAaPQ)EBC3070786(PPN)168324083(EXLCZ)99340000000010277720121223d2013 uy 0engurnn|008mamaatxtccrGuts of surfaces and the colored Jones polynomial /David Futer, Efstratia Kalfagianni, Jessica Purcell1st ed. 2013.Heidelberg ;New York Springerc20131 online resource (X, 170 p. 62 illus., 45 illus. in color.) Lecture notes in mathematics,1617-9692 ;2069Bibliographic Level Mode of Issuance: Monograph3-642-33301-X Includes bibliographical references (p. 163-166) and index.1 Introduction -- 2 Decomposition into 3–balls -- 3 Ideal Polyhedra -- 4 I–bundles and essential product disks -- 5 Guts and fibers -- 6 Recognizing essential product disks -- 7 Diagrams without non-prime arcs -- 8 Montesinos links -- 9 Applications -- 10 Discussion and questions.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.Lecture notes in mathematics (Springer-Verlag) ;2069.Knot theoryThree-manifolds (Topology)Complex manifoldsGeometry, HyperbolicKnot theory.Three-manifolds (Topology)Complex manifolds.Geometry, Hyperbolic.514.2242Futer David479687Kalfagianni Efstratia521607Purcell Jessica521608MiAaPQMiAaPQMiAaPQBOOK9910438143803321Guts of surfaces and the colored Jones polynomial836978UNINA