000 03302nam a22005175i 4500
001 978-3-642-33302-6
003 DE-He213
005 20160624101838.0
007 cr nn 008mamaa
008 121227s2013 gw | s |||| 0|eng d
020 _a9783642333026
_9978-3-642-33302-6
024 7 _a10.1007/978-3-642-33302-6
_2doi
050 4 _aQA613-613.8
050 4 _aQA613.6-613.66
072 7 _aPBMS
_2bicssc
072 7 _aPBPH
_2bicssc
072 7 _aMAT038000
_2bisacsh
082 0 4 _a514.34
_223
100 1 _aFuter, David.
_eauthor.
245 1 0 _aGuts of Surfaces and the Colored Jones Polynomial
_h[electronic resource] /
_cby David Futer, Efstratia Kalfagianni, Jessica Purcell.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aX, 170 p. 62 illus., 45 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2069
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aCell aggregation
_xMathematics.
650 1 4 _aMathematics.
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
650 2 4 _aHyperbolic Geometry.
700 1 _aKalfagianni, Efstratia.
_eauthor.
700 1 _aPurcell, Jessica.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642333019
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2069
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-33302-6
942 _2EBK2011
_cEBK
999 _c31305
_d31305