000 | 03302nam a22005175i 4500 | ||
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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 |
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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. |
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300 |
_aX, 170 p. 62 illus., 45 illus. in color. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
||
490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2069 |
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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. |
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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. |
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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 |
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999 |
_c31305 _d31305 |