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Journal of Mathematics
Volume 2013 (2013), Article ID 407068, 25 pages
http://dx.doi.org/10.1155/2013/407068
Research Article

Twin TQFTs and Frobenius Algebras

Department of Mathematics, California State University, Fresno, 5245 North Backer Avenue M/S PB 108, Fresno, CA 93740-8001, USA

Received 12 November 2012; Accepted 16 December 2012

Academic Editor: Roberto A. Kraenkel

Copyright © 2013 Carmen Caprau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Abrams, “Two-dimensional topological quantum field theories and Frobenius algebras,” Journal of Knot Theory and Its Ramifications, vol. 5, no. 5, pp. 569–587, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. Dijkgraaf, A geometric approach to two dimensional conformal field theory [Ph.D. thesis], University of Utrecht, Utrecht, The Netherlands, 1989.
  3. S. Sawin, “Direct sum decompositions and indecomposable TQFTs,” Journal of Mathematical Physics, vol. 36, no. 12, pp. 6673–6680, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. Kock, Frobenius Algebras and 2D Topological Quantum Field Theories, vol. 59 of London Mathematical Society Student Texts, Cambridge University Press, Cambridge, UK, 2004. View at MathSciNet
  5. A. D. Lauda and H. Pfeiffer, “Open-closed strings: two-dimensional extended TQFTs and Frobenius algebras,” Topology and Its Applications, vol. 155, no. 7, pp. 623–666, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. C. L. Caprau, “ sl (2) tangle homology with a parameter and singular cobordisms,” Algebraic & Geometric Topology, vol. 8, no. 2, pp. 729–756, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. D. Bar-Natan, “Khovanov's homology for tangles and cobordisms,” Geometry and Topology, vol. 9, pp. 1443–1499, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Khovanov, “sl(3) link homology,” Algebraic & Geometric Topology, vol. 4, pp. 1045–1081, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. C. Caprau, “The universal sl(2) cohomology via webs and foams,” Topology and its Applications, vol. 156, no. 9, pp. 1684–1702, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Khovanov, “Link homology and Frobenius extensions,” Fundamenta Mathematicae, vol. 190, pp. 179–190, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. Bar-Natan, “On Khovanov's categorification of the Jones polynomial,” Algebraic & Geometric Topology, vol. 2, pp. 337–370, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Khovanov, “A categorification of the Jones polynomial,” Duke Mathematical Journal, vol. 101, no. 3, pp. 359–426, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. E. S. Lee, “An endomorphism of the Khovanov invariant,” Advances in Mathematics, vol. 197, no. 2, pp. 554–586, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. D. Clark, S. Morrison, and K. Walker, “Fixing the functoriality of Khovanov homology,” Geometry & Topology, vol. 13, no. 3, pp. 1499–1582, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. C. Caprau, “On the sl(2) foam cohomology computations,” Journal of Knot Theory and Its Ramifications, vol. 18, no. 9, pp. 1313–1328, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. M. L. Laplaza, “Coherence for categories with group structure: an alternative approach,” Journal of Algebra, vol. 84, no. 2, pp. 305–323, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. L. Kadison, New Examples of Frobenius Extensions, vol. 14 of University Lecture Series, American Mathematical Society, Providence, RI, USA, 1999. View at MathSciNet
  18. A. D. Lauda and H. Pfeiffer, “Open-closed TQFTS extend Khovanov homology from links to tangles,” Journal of Knot Theory and Its Ramifications, vol. 18, no. 1, pp. 87–150, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet