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Book Review

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Book Information:

Author: Vladimir Turaev
Title: Homotopy quantum field theory
Additional book information: EMS Tracts in Mathematics, 10, European Mathematical Society (EMS), Zurich, 2010, xiv+276 pp., ISBN 978-3-03719-086-9, $78.00, hardcover

References [Enhancements On Off] (What's this?)

  • 1. M. Brightwell and P. Turner, Representations of the homotopy surface category of a simply connected space, J. Knot Theory and its Ramifications 9 (2000), no. 7, 855-864. MR 1780591 (2001i:57045)
  • 2. M. Fukuma, S. Hosono, and H. Kawai, Lattice topological field theory in two dimensions, Comm. Math. Phys. 161 (1994), 157-175. MR 1266073 (95b:81179)
  • 3. R. M. Kaufmann, Orbifolding Frobenius algebras, Int. J. Math. 14 (2003), no. 6, 573-617. MR 1997832 (2005b:57057)
  • 4. J. Kock, Frobenius algebras and 2-d topological quantum field theories, London Mathematical Society Student Texts, no. 59, Cambridge University Press, Cambridge, 2003.
  • 5. J. Lurie, On the classification of topological field theories, 2009. http://arXiv.org/ abs/0905.0465
  • 6. G. W. Moore and G. Segal, D-branes and k-theory in 2d topological field theory, 2006.
  • 7. T. Porter and V. Turaev, Formal homotopy quantum field theories, I: Formal maps and crossed $ \mathcal{C}$-algebras, Journal of Homotopy and Related Structures 3 (2008), no. 1, 113-159. MR 2426178 (2009e:18025)
  • 8. G. Rodrigues, Homotopy quantum field theories and the homotopy cobordism category in dimension $ 1 + 1$, J. Knot Theory and its Ramifications 12 (2003), 287-317. MR 1983087 (2004e:57039)
  • 9. V. G. Turaev, Quantum invariants of knots and $ 3$-manifolds, de Gruyter Studies in Mathematics, vol. 18, Walter de Gruyter, 1994. MR 1292673 (95k:57014)
  • 10. -, Homotopy field theory in dimension $ 2$ and group-algebras, arXiv.org:math/9910010, 1999.
  • 11. -, Homotopy field theory in dimension $ 3$ and crossed group-categories, arXiv.org: math/ 0005291, 2000.

Review Information:

Reviewer: Timothy Porter
Affiliation: University of Bangor, United Kingdom
Email: t.porter@bangor.ac.uk
Journal: Bull. Amer. Math. Soc. 49 (2012), 337-345
MSC (2010): Primary 57-02
DOI: https://doi.org/10.1090/S0273-0979-2011-01351-9
Published electronically: September 13, 2011
Review copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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