previous :: next
Topological quantum field theories for surfaces with spin structure
C. Blanchet and G. Masbaum
Source: Duke Math. J. Volume 82, Number 2
(1996), 229-267.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077245032
Mathematical Reviews number (MathSciNet): MR1387228
Zentralblatt MATH identifier: 0854.57025
Digital Object Identifier: doi:10.1215/S0012-7094-96-08211-3
References
[1] M. F. Atiyah, Topological quantum field theories, Inst. Hautes Études Sci. Publ. Math. (1988), no. 68, 175–186 (1989).
Mathematical Reviews (MathSciNet): MR90e:57059
Zentralblatt MATH: 0692.53053
Digital Object Identifier: doi:10.1007/BF02698547
[2] M. F. Atiyah, Riemann surfaces and spin structures, Ann. Sci. École Norm. Sup. (4) 4 (1971), 47–62.
Mathematical Reviews (MathSciNet): MR44:3350
Zentralblatt MATH: 0212.56402
[3] M. F. Atiyah, On framings of $3$-manifolds, Topology 29 (1990), no. 1, 1–7.
Mathematical Reviews (MathSciNet): MR91g:57025
Zentralblatt MATH: 0716.57011
Digital Object Identifier: doi:10.1016/0040-9383(90)90021-B
[4] N. A. Baas, On bordism theory of manifolds with singularities, Math. Scand. 33 (1973), 279–302 (1974).
Mathematical Reviews (MathSciNet): MR49:11547b
Zentralblatt MATH: 0281.57027
[5] C. Blanchet, Invariants on three-manifolds with spin structure, Comment. Math. Helv. 67 (1992), no. 3, 406–427.
Mathematical Reviews (MathSciNet): MR94f:57003
Zentralblatt MATH: 0771.57005
Digital Object Identifier: doi:10.1007/BF02566511
[6] C. Blanchet, N. Habegger, G. Masbaum, and P. Vogel, Three-manifold invariants derived from the Kauffman bracket, Topology 31 (1992), no. 4, 685–699.
Mathematical Reviews (MathSciNet): MR94a:57010
Zentralblatt MATH: 0771.57004
Digital Object Identifier: doi:10.1016/0040-9383(92)90002-Y
[7] C. Blanchet, N. Habegger, G. Masbaum, and P. Vogel, Remarks on the three-manifold invariants $\theta\sb p$, Operator algebras, mathematical physics, and low-dimensional topology (Istanbul, 1991) eds. R. Herman and B. Tanbay, Res. Notes Math., vol. 5, A K Peters, Wellesley, MA, 1993, pp. 39–59.
Mathematical Reviews (MathSciNet): MR95j:57015
Zentralblatt MATH: 0839.57013
[8] C. Blanchet, N. Habegger, G. Masbaum, and P. Vogel, Topological quantum field theories derived from the Kauffman bracket, Topology 34 (1995), no. 4, 883–927.
Mathematical Reviews (MathSciNet): MR96i:57015
Zentralblatt MATH: 0887.57009
Digital Object Identifier: doi:10.1016/0040-9383(94)00051-4
[9] P. M. Gilmer, Link cobordism in rational homology $3$-spheres, J. Knot Theory Ramifications 2 (1993), no. 3, 285–320.
Mathematical Reviews (MathSciNet): MR94m:57012
Zentralblatt MATH: 0797.57003
Digital Object Identifier: doi:10.1142/S0218216593000179
[10] D. Johnson, Spin structures and quadratic forms on surfaces, J. London Math. Soc. (2) 22 (1980), no. 2, 365–373.
Mathematical Reviews (MathSciNet): MR81m:57015
Zentralblatt MATH: 0454.57011
Digital Object Identifier: doi:10.1112/jlms/s2-22.2.365
[11] V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25.
Mathematical Reviews (MathSciNet): MR84d:46097
Zentralblatt MATH: 0508.46040
Digital Object Identifier: doi:10.1007/BF01389127
[12] V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 1, 103–111.
Mathematical Reviews (MathSciNet): MR86e:57006
Zentralblatt MATH: 0564.57006
Digital Object Identifier: doi:10.1090/S0273-0979-1985-15304-2
Project Euclid: euclid.bams/1183552338
[13] L. H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), no. 3, 395–407.
Mathematical Reviews (MathSciNet): MR88f:57006
Zentralblatt MATH: 0622.57004
Digital Object Identifier: doi:10.1016/0040-9383(87)90009-7
[14] R. Kirby, A calculus for framed links in $S\sp3$, Invent. Math. 45 (1978), no. 1, 35–56.
Mathematical Reviews (MathSciNet): MR57:7605
Zentralblatt MATH: 0377.55001
Digital Object Identifier: doi:10.1007/BF01406222
[15] R. Kirby, The topology of $4$-manifolds, Lecture Notes in Mathematics, vol. 1374, Springer-Verlag, Berlin, 1989.
Mathematical Reviews (MathSciNet): MR90j:57012
Zentralblatt MATH: 0668.57001
[16] R. Kirby and P. Melvin, The $3$-manifold invariants of Witten and Reshetikhin-Turaev for $\rm sl(2,\bf C)$, Invent. Math. 105 (1991), no. 3, 473–545.
Mathematical Reviews (MathSciNet): MR92e:57011
Zentralblatt MATH: 0745.57006
Digital Object Identifier: doi:10.1007/BF01232277
[17] T. Kohno, Topological invariants for $3$-manifolds using representations of mapping class groups. I, Topology 31 (1992), no. 2, 203–230.
Mathematical Reviews (MathSciNet): MR94c:57031
Zentralblatt MATH: 0762.57011
Digital Object Identifier: doi:10.1016/0040-9383(92)90016-B
[18] W. B. R. Lickorish, Three-manifolds and the Temperley-Lieb algebra, Math. Ann. 290 (1991), no. 4, 657–670.
Mathematical Reviews (MathSciNet): MR92e:57014
Zentralblatt MATH: 0739.57004
Digital Object Identifier: doi:10.1007/BF01459265
[19] W. B. R. Lickorish, Calculations with the Temperley-Lieb algebra, Comment. Math. Helv. 67 (1992), no. 4, 571–591.
Mathematical Reviews (MathSciNet): MR94c:57032
Zentralblatt MATH: 0779.57008
Digital Object Identifier: doi:10.1007/BF02566519
[20] S. MacLane, Categories for the working mathematician, Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1971.
Mathematical Reviews (MathSciNet): MR50:7275
Zentralblatt MATH: 0705.18001
[21] G. Masbaum, Introduction to Spin TQFT, to appear in Proceedings of the 1993 Georgia International Topology Conference at Athens, Georgia.
Mathematical Reviews (MathSciNet): MR1470728
Zentralblatt MATH: 0889.57025
[22] G. Masbaum, Spin TQFT and the Birman-Craggs homomorphisms, Turkish J. Math. 19 (1995), no. 2, 189–199, Proceedings of Third Gökova Geometry-Topology Conference, tübitak, 1994.
Mathematical Reviews (MathSciNet): MR96i:57018
Zentralblatt MATH: 0878.57016
[23] G. Masbaum, in preparation.
[24] G. Masbaum and P. Vogel, $3$-valent graphs and the Kauffman bracket, Pacific J. Math. 164 (1994), no. 2, 361–381.
Mathematical Reviews (MathSciNet): MR95e:57003
Zentralblatt MATH: 0838.57007
Project Euclid: euclid.pjm/1102622100
[25] G. Masbaum and P. Vogel, Verlinde formulae for surfaces with spin structure, Geometric topology (Haifa, 1992), Contemp. Math., vol. 164, Amer. Math. Soc., Providence, RI, 1994, pp. 119–137.
Mathematical Reviews (MathSciNet): MR95d:57016
Zentralblatt MATH: 0824.57012
[26] J. Milnor, Spin structures on manifolds, Enseignement Math. (2) 9 (1963), 198–203.
Mathematical Reviews (MathSciNet): MR28:622
Zentralblatt MATH: 0116.40403
[27] H. Morton and P. Strickland, Satellites and surgery invariants, Knots 90 (Osaka, 1990) ed. A. Kawauchi, de Gruyter, Berlin, 1992, pp. 47–66.
Mathematical Reviews (MathSciNet): MR94d:57022
Zentralblatt MATH: 0763.57006
[28] N. Yu. Reshetikhin and V. G. Turaev, Invariants of $3$-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), no. 3, 547–597.
Mathematical Reviews (MathSciNet): MR92b:57024
Zentralblatt MATH: 0725.57007
Digital Object Identifier: doi:10.1007/BF01239527
[29] V. G. Turaev, State sum models in low-dimensional topology, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), Math. Soc. Japan, Tokyo, 1991, pp. 689–698.
Mathematical Reviews (MathSciNet): MR93g:57015
Zentralblatt MATH: 0744.57007
[30] H. Wenzl, On sequences of projections, C. R. Math. Rep. Acad. Sci. Canada 9 (1987), no. 1, 5–9.
Mathematical Reviews (MathSciNet): MR88k:46070
Zentralblatt MATH: 0622.47019
[31] H. Wenzl, Braids and invariants of $3$-manifolds, Invent. Math. 114 (1993), no. 2, 235–275.
Mathematical Reviews (MathSciNet): MR94i:57021
Zentralblatt MATH: 0804.57007
Digital Object Identifier: doi:10.1007/BF01232670
[32] E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), no. 3, 351–399.
Mathematical Reviews (MathSciNet): MR90h:57009
Zentralblatt MATH: 0667.57005
Digital Object Identifier: doi:10.1007/BF01217730
Project Euclid: euclid.cmp/1104178138
[33] G. Wright, The Reshetikhin-Turaev representation of the mapping class group, J. Knot Theory Ramifications 3 (1994), no. 4, 547–574.
Mathematical Reviews (MathSciNet): MR95k:57028
Zentralblatt MATH: 0878.57017
Digital Object Identifier: doi:10.1142/S021821659400040X
previous :: next
Duke Mathematical Journal
