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1998 | 42 | 1 | 119-127
Tytuł artykułu

A TQFT for Wormhole cobordisms over the field of rational functions

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Języki publikacji
EN
Abstrakty
EN
We consider a cobordism category whose morphisms are punctured connected sums of $S^1 × S^2$'s (wormhole spaces) with embedded admissibly colored banded trivalent graphs. We define a TQFT on this cobordism category over the field of rational functions in an indeterminant A. For r large, we recover, by specializing A to a primitive 4rth root of unity, the Witten-Reshetikhin-Turaev TQFT restricted to links in wormhole spaces. Thus, for r large, the rth Witten-Reshetikhin-Turaev invariant of a link in some wormhole space, properly normalized, is the value of a certain rational function at $e^{(πi)/(2r)}$. We relate our work to Hoste and Przytycki's calculation of the Kauffman bracket skein module of $S^1 × S^2$.
Słowa kluczowe
Rocznik
Tom
42
Numer
1
Strony
119-127
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803, U.S.A.
Bibliografia
  • [A] M. F. Atiyah, Topological quantum field theories, Inst. Hautes Études Sci. Publ. Math. 68 (1988), 175-186.
  • [BHMV] C. Blanchet, N. Habegger, G. Masbaum, P. Vogel, Topological Quantum Field Theories Derived from the Kauffman Bracket, Topology 34 (1995), 883-927.
  • [G] P. Gilmer, Invariants for 1-dimensional cohomology classes arising from TQFT, Top. and its Appl. 75 (1997), 217-259.
  • [HP] J. Hoste, J. Przytycki, The Kauffman Bracket Skein Module of $S^1 × S^2$, Math. Zeit. 220 (1995), 65-73.
  • [J] V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bulletin AMS 12 (1985), 103-111.
  • [K] L. H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), 395-407.
  • [KL] L. H. Kauffman, S. Lins, Temperley Lieb recoupling theory and invariants of $3$-manifolds, Annals of Math Studies 91994), Princeton Univ. Press, Princeton N.J.
  • [Ki] R. Kirby, The Topology of 4-manifolds, Springer Lecture Notes in Math. 1374.
  • [La] R. Lawrence, Asymptotic expansions of Witten-Reshetikhin-Turaev invariants for some simple 3-manifolds, J. Math. Phys. 36 (1995), 6106-6129.
  • [L] W. B. R. Lickorish, The skein Method for three manifolds, J. of Knot Th. and its Ramif. 2 (1993), 171-194.
  • [MV] G. Masbaum, P. Vogel, Verlinde Formulae for surfaces with spin structure, Geometric Topology, Joint U.S. Israel Workshop on Geometric Topology June 10-16, 1992 Technion, Haifa, Israel Contemporary Mathematics 164 (Gordon, Moriah, Waynryb, ed.), American Math. Soc., 1994, 119-137.
  • [RT] N. Reshetikhin, V. Turaev, Invariants of 3-manifolds via link-polynomials and quantum groups, Invent. Math. 103 (1991), 547-597.
  • [R] J. Roberts, Skein Theory and Turaev-Viro invariants, Topology 34 (1995), 771-787.
  • [W] E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 (1989), 351-399.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv42i1p119bwm
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