Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Buchtitelbild

2013 | OriginalPaper | Buchkapitel

1. Introduction

verfasst von : David Futer, Efstratia Kalfagianni, Jessica Purcell

Erschienen in: Guts of Surfaces and the Colored Jones Polynomial

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In the last 3 decades, there has been significant progress in 3-dimensional topology, due in large part to the application of new techniques from other areas of mathematics and from physics. On the one hand, ideas from geometry have led to geometric decompositions of 3-manifolds and to invariants such as the A-polynomial and hyperbolic volume. On the other hand, ideas from quantum physics have led to the development of invariants such as the Jones polynomial and colored Jones polynomials.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Nächstes Kapitel Decomposition into 3-Balls
Literatur
2.
Adams, C.C.: Noncompact Fuchsian and quasi-Fuchsian surfaces in hyperbolic 3-manifolds. Algebr. Geomet. Topology 7, 565–582 (2007)MATHCrossRef
3.
Agol, I.: Lower bounds on volumes of hyperbolic Haken 3-manifolds. arXiv:math/9906182
4.
Agol, I.: The virtual Haken conjecture. arXiv:1204.2810. With an appendix by Ian Agol, Daniel Groves, and Jason Manning
5.
6.
Agol, I., Storm, P.A., Thurston, W.P.: Lower bounds on volumes of hyperbolic Haken 3-manifolds. J. Am. Math. Soc. 20(4), 1053–1077 (2007). With an appendix by Nathan Dunfield
7.
Andreev, E.M.: Convex polyhedra in Lobačevskiĭ spaces. Mat. Sb. (N.S.) 81(123), 445–478 (1970)
8.
Andreev, E.M.: Convex polyhedra of finite volume in Lobačevskiĭ space. Mat. Sb. (N.S.) 83(125), 256–260 (1970)
10.
Atiyah, M.: The Geometry and Physics of Knots. Lezioni Lincee [Lincei Lectures]. Cambridge University Press, Cambridge (1990). doi:10.1017/CBO9780511623868
17.
18.
Champanerkar, A., Kofman, I., Patterson, E.: The next simplest hyperbolic knots. J. Knot Theor. Ramifications 13(7), 965–987 (2004)MathSciNetMATHCrossRef
19.
Cromwell, P.R.: Homogeneous links. J. Lond. Math. Soc. (2) 39(3), 535–552 (1989). doi:10.1112/jlms/s2-39.3.535
20.
Culler, M., Shalen, P.B.: Volumes of hyperbolic Haken manifolds. I. Invent. Math. 118(2), 285–329 (1994). doi:10.1007/BF01231535MathSciNetMATHCrossRef
21.
Dasbach, O.T., Futer, D., Kalfagianni, E., Lin, X.S., Stoltzfus, N.W.: The Jones polynomial and graphs on surfaces. J. Combin. Theor. Ser. B 98(2), 384–399 (2008)MathSciNetMATHCrossRef
23.
24.
Dasbach, O.T., Lin, X.S.: A volume-ish theorem for the Jones polynomial of alternating knots. Pac. J. Math. 231(2), 279–291 (2007)MathSciNetMATHCrossRef
25.
28.
Freyd, P., Yetter, D.N., Hoste, J., Lickorish, W.B.R., Millett, K.C., Ocneanu, A.: A new polynomial invariant of knots and links. Bull. Am. Math. Soc. (N.S.) 12(2), 239–246 (1985). doi:10.1090/S0273-0979-1985-15361-3
29.
Futer, D.: Fiber detection for state surfaces. arXiv:1201.1643 (2012)
31.
Futer, D., Kalfagianni, E., Purcell, J.S.: Quasifuchsian state surfaces. ArXiv:1209.5719 (2012)
32.
Futer, D., Kalfagianni, E., Purcell, J.S.: Dehn filling, volume, and the Jones polynomial. J. Differ. Geom. 78(3), 429–464 (2008)MathSciNetMATH
33.
Futer, D., Kalfagianni, E., Purcell, J.S.: Symmetric links and Conway sums: volume and Jones polynomial. Math. Res. Lett. 16(2), 233–253 (2009)MathSciNetMATH
34.
Futer, D., Kalfagianni, E., Purcell, J.S.: Cusp areas of Farey manifolds and applications to knot theory. Int. Math. Res. Not. IMRN 2010(23), 4434–4497 (2010)MathSciNetMATH
35.
Futer, D., Kalfagianni, E., Purcell, J.S.: On diagrammatic bounds of knot volumes and spectral invariants. Geometriae Dedicata 147, 115–130 (2010). doi:10.1007/s10711-009-9442-6MathSciNetMATHCrossRef
36.
Futer, D., Kalfagianni, E., Purcell, J.S.: Slopes and colored Jones polynomials of adequate knots. Proc. Am. Math. Soc. 139, 1889–1896 (2011)MathSciNetMATHCrossRef
37.
Futer, D., Kalfagianni, E., Purcell, J.S.: Jones polynomials, volume, and essential knot surfaces: a survey. In: Proceedings of Knots in Poland III. Banach Center Publications (to appear)
41.
Garoufalidis, S.: The degree of a q-holonomic sequence is a quadratic quasi-polynomial. Electron. J. Combin. 18(2), Paper 4, 23 (2011)
42.
43.
Garoufalidis, S., Lê, T.T.Q.: The colored Jones function is q-holonomic. Geom. Topology 9, 1253–1293 (electronic) (2005). doi:10.2140/gt.2005.9.1253
44.
Gromov, M.: Volume and bounded cohomology. Inst. Hautes Études Sci. Publ. Math. (56), 5–99 (1982/1983)
46.
47.
Jaco, W.H., Shalen, P.B.: Seifert fibered spaces in 3-manifolds. Mem. Am. Math. Soc. 21(220), viii+192 (1979)
48.
Johannson, K.: Homotopy Equivalences of 3-Manifolds with Boundaries. Lecture Notes in Mathematics, vol. 761. Springer, Berlin (1979)
49.
Jones, V.F.R.: A polynomial invariant for knots via von Neumann algebras. Bull. Am. Math. Soc. (N.S.) 12(1), 103–111 (1985). doi:10.1090/S0273-0979-1985-15304-2
50.
Jones, V.F.R.: Hecke algebra representations of braid groups and link polynomials. Ann. Math. (2) 126(2), 335–388 (1987)
51.
Jørgensen, T.: Compact 3-manifolds of constant negative curvature fibering over the circle. Ann. Math. (2) 106(1), 61–72 (1977)
52.
Kashaev, R.M.: Quantum dilogarithm as a 6j-symbol. Mod. Phys. Lett. A 9(40), 3757–3768 (1994). doi:10.1142/S0217732394003610MathSciNetMATHCrossRef
53.
Kashaev, R.M.: A link invariant from quantum dilogarithm. Mod. Phys. Lett. A 10(19), 1409–1418 (1995). doi:10.1142/S0217732395001526MathSciNetMATHCrossRef
54.
55.
56.
57.
Kuessner, T.: Guts of surfaces in punctured-torus bundles. Arch. Math. (Basel) 86(2), 176–184 (2006). doi:10.1007/s00013-005-1097-4
58.
Lackenby, M.: The volume of hyperbolic alternating link complements. Proc. Lond. Math. Soc. (3) 88(1), 204–224 (2004). With an appendix by Ian Agol and Dylan Thurston
60.
Lickorish, W.B.R.: An Introduction to Knot Theory. Graduate Texts in Mathematics, vol. 175. Springer, New York (1997)
61.
Lickorish, W.B.R., Thistlethwaite, M.B.: Some links with nontrivial polynomials and their crossing-numbers. Comment. Math. Helv. 63(4), 527–539 (1988)MathSciNetMATHCrossRef
63.
Manchón, P.M.G.: Extreme coefficients of Jones polynomials and graph theory. J. Knot Theor. Ramifications 13(2), 277–295 (2004). doi:10.1142/S0218216504003135MATHCrossRef
64.
Menasco, W.W.: Polyhedra representation of link complements. In: Low-Dimensional Topology (San Francisco, CA, 1981). Contemporary Mathematics, vol. 20, pp. 305–325. American Mathematical Society, Providence (1983)
65.
Menasco, W.W.: Closed incompressible surfaces in alternating knot and link complements. Topology 23(1), 37–44 (1984). doi:10.1016/0040-9383(84)90023-5MathSciNetMATHCrossRef
68.
Miyamoto, Y.: Volumes of hyperbolic manifolds with geodesic boundary. Topology 33(4), 613–629 (1994). doi:10.1016/0040-9383(94)90001-9MathSciNetMATHCrossRef
69.
Morgan, J., Tian, G.: Ricci Flow and the Poincaré Conjecture. Clay Mathematics Monographs, vol. 3. American Mathematical Society, Providence (2007)
71.
Mostow, G.D.: Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms. Inst. Hautes Études Sci. Publ. Math. (34), 53–104 (1968)MathSciNetMATHCrossRef
72.
Murakami, H.: An introduction to the volume conjecture. In: Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory. Contemporary Mathematics, vol. 541, pp. 1–40. American Mathematical Society, Providence (2011). doi:10.1090/conm/541/10677
73.
Murakami, H., Murakami, J.: The colored Jones polynomials and the simplicial volume of a knot. Acta Math. 186(1), 85–104 (2001)MathSciNetMATHCrossRef
75.
76.
77.
Ozsváth, P., Szabó, Z.: Holomorphic disks and genus bounds. Geom. Topology 8, 311–334 (2004). doi:10.2140/gt.2004.8.311MATHCrossRef
78.
Ozsváth, P., Szabó, Z.: Link Floer homology and the Thurston norm. J. Am. Math. Soc. 21(3), 671–709 (2008). doi:10.1090/S0894-0347-08-00586-9MATHCrossRef
79.
Perelman, G.: The entropy formula for the Ricci flow and its geometric applications. arXiv:math.DG/0211159 (2002)
80.
Perelman, G.: Ricci flow with surgery on three-manifolds. arXiv:math.DG/0303109 (2003)
82.
84.
Reshetikhin, N., Turaev, V.G.: Ribbon graphs and their invariants derived from quantum groups. Comm. Math. Phys. 127(1), 1–26 (1990)MathSciNetMATHCrossRef
85.
Reshetikhin, N., Turaev, V.G.: Invariants of 3-manifolds via link polynomials and quantum groups. Invent. Math. 103(3), 547–597 (1991). doi:10.1007/BF01239527MathSciNetMATHCrossRef
86.
87.
90.
91.
Stoimenow, A.: On the crossing number of semi-adequate links. Forum Math. (in press). doi:10.1515/forum-2011-0121
92.
Thistlethwaite, M.B.: On the Kauffman polynomial of an adequate link. Invent. Math. 93(2), 285–296 (1988). doi:10.1007/BF01394334MathSciNetMATHCrossRef
93.
Thurston, W.P.: Three-dimensional manifolds, Kleinian groups and hyperbolic geometry. Bull. Am. Math. Soc. (N.S.) 6(3), 357–381 (1982)
94.
Thurston, W.P.: A norm for the homology of 3-manifolds. Mem. Am. Math. Soc. 59(339), i–vi and 99–130 (1986)
96.
Witten, E.: 2 + 1-dimensional gravity as an exactly soluble system. Nucl. Phys. B 311(1), 46–78 (1988/1989). doi:10.1016/0550-3213(88)90143-5
97.
Metadaten
Titel
Introduction
verfasst von
David Futer
Efstratia Kalfagianni
Jessica Purcell
Copyright-Jahr
2013
Verlag
Springer Berlin Heidelberg
Buch
Guts of Surfaces and the Colored Jones Polynomial

Print ISBN: 978-3-642-33301-9

Electronic ISBN: 978-3-642-33302-6

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-3-642-33302-6_1

Premium Partner

    Bildnachweise