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100   $a20121227d2013      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aGuts of Surfaces and the Colored Jones Polynomial$b[electronic resource] /$fby David Futer, Efstratia Kalfagianni, Jessica Purcell
205   $a1st ed. 2013.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013.
215   $a1 online resource (X, 170 p. 62 illus., 45 illus. in color.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2069
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-33301-X 
320   $aIncludes bibliographical references (p. 163-166) and index.
327   $a1 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.
330   $aThis monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for the knot; in particular, the surface is a fiber if and only if a particular coefficient vanishes. We also relate hyperbolic volume to colored Jones polynomials. Our method is to generalize the checkerboard decompositions of alternating knots. Under mild diagrammatic hypotheses, we show that these surfaces are essential, and obtain an ideal polyhedral decomposition of their complement. We use normal surface theory to relate the pieces of the JSJ decomposition of the  complement to the combinatorics of certain surface spines (state graphs). Since state graphs have previously appeared in the study of Jones polynomials, our method bridges the gap between quantum and geometric knot invariants.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2069
606   $aManifolds (Mathematics)
606   $aComplex manifolds
606   $aHyperbolic geometry
606   $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027
606   $aHyperbolic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21030
615  0$aManifolds (Mathematics).
615  0$aComplex manifolds.
615  0$aHyperbolic geometry.
615 14$aManifolds and Cell Complexes (incl. Diff.Topology).
615 24$aHyperbolic Geometry.
676   $a514.34
700   $aFuter$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$0479687
702   $aKalfagianni$b Efstratia$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aPurcell$b Jessica$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a996466472903316
996   $aGuts of Surfaces and the Colored Jones Polynomial$92516806
997   $aUNISA