On algebraic structures implicit in topological quantum field theories

Journal of Knot Theory and its Ramifications

Volumn 8, Issue 2, 1999, Pages 125-163

  Crane, Louis ^a   Yetter, David ^a  

^a KANSAS STATE UNIVERSITY   (United States)

Author keywords

Crossed bimodule; Hopf algebra; Monoidal category; Topological Quantum Field Theory

Indexed keywords

EID: 0033454552     PISSN: 02182165     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218216599000109     Document Type: Article

References (30)

1. M. Atiyah, Topological Quantum Field Theory, Cambridge University Press, 1990.
2. E. Witten, Topological quantum field theory, Comm. Math. Phys. 117, 353-386, 1988.
3. R. Dijkgraf and E. Witten, Topological Gauge Theories and Group Cohomology, Commun. Math. Phys 129 393-429, 1990
4. M. Fukama, S. Hosong, and H. Kawai, Lattice Topological Field Theory, preprint, 1993
5. N. Reshetikhin and V.G. Turaev, Invariants of 3-manifold via link polynomials and quantum groups, Invent. math. 103 547-597, 1991.
6. L. Crane, 2-d Physics and 3-d Topology, Commun. Math. Phys. 135 615-640, 1991.
7. V. Turaev and O. Viro, State Sum Invariants of 3-manifolds and Quantum 6j symbols , Topology 31 865-902, 1992
8. K. Walker, On Wittens 3 Manifold Invariants, unpublished
9. D.N. Yetter, State-sum invariants of 3-manifolds associated to artinian semisimple tortile categories, Top. and its App. 58 47-80, 1994.
10. G. Kuperberg , Involutory Hopf Algebras and Three-manifold Invariants, Int. J. Math. p41-61, 1989 See also : Non-Involutory Hopf algebras and 3-Manifold Invariants, preprint, U. of Chicago math department
11. G. Kuperberg , Involutory Hopf Algebras and Three-manifold Invariants, Int. J. Math. p41-61, 1989 See also : Non-Involutory Hopf algebras and 3-Manifold Invariants, preprint, U. of Chicago math department
12. S. Chung, M. Fukama, and A. Shapere, , Structure of Topological Field Theories in Three Dimensions preprint
13. L. Crane and Igor B. Frenkel Four Dimensional Topological Quantum Field Theory, Hopf Categories, and the Canonical Bases J. Math Physics, special issue, p5136, 1994
14. G. Lusztig, Introduction to Quantum Groups, Birkhauser, 1993
15. E. Witten Monopoles and Four Manifolds, hep-th preprint 9411102
16. C. Taubes, personal communication
17. M. Kapranov and V. Voevodsky, Braided Monoidal 2-Categories, 2-Vector Spaces and Zamolodchikov's Tetrahedra Equation, preprint. See also: 2-Categories and Zamolodchikov Tetrahedra Equations, Proceedings of Symposia in Pure Mathematics 56, Am. Math. Soc. 1994, 177-259.
18. M. Kapranov and V. Voevodsky, Braided Monoidal 2-Categories, 2-Vector Spaces and Zamolodchikov's Tetrahedra Equation, preprint. See also: 2-Categories and Zamolodchikov Tetrahedra Equations, Proceedings of Symposia in Pure Mathematics 56, Am. Math. Soc. 1994, 177-259.
19. J. Benabou, Introduction to bicategories, in Reports of the Midwest Category Seminar, Lecture Notes in Math 47, Springer-Verlag, 1967, 1-77.
20. R. Gordon, A.J. Power, and R. Street, Coherence for tricategories, preprint, 1993.
21. D.N. Yetter, Categorical linear algebra - A setting for questions from physics and low-dimensional topology, preprint, 1993.
22. D. Kazhdan, lectures at Harvard University, Fall Semester 1990.
23. R. Lawrence, Triangulations, categories and extended topological field theories, in Quantum Topology (R.A. Baadhio and L.H. Kauffman, eds.) World Scientific 1999, 191-208.
24. S. Majid, Algebras and Hopf algebras in braided categories, in Advances in Hopf Algebras, Plenum 1993.
25. D.N. Yetter, Quantum groups and representations of monoidal categories, Math. Proc. Camb. Phil. Soc. 108 261-290, 1990.
26. D. Radford and J. Towber, Yetter-Drinfel'd categories associated to an arbitrary bialgebra, J. Pure and App. Alg. 87 259-279, 1993.
27. S. Mac Lane, Categories for the Working Mathematician, Springer-Verlag, 1971.
28. M. Laplaza, Coherence for distributivity, Lecture Notes in Math 281, Springer-Verlag, 1972, 29-65.
29. L. Crane and Igor B. Frenkel, On The Dimensional Ladder, to appear.
30. D.N. Yetter, Portrait of the Handle as a Self-Dual Hopf Algebra, preprint, November 1995.