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Book Review

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MathSciNet review: 2919689
Full text of review: PDF   This review is available free of charge.
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

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References
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  • Ralph M. Kaufmann, Orbifolding Frobenius algebras, Internat. J. Math. 14 (2003), no. 6, 573–617. MR 1997832, DOI https://doi.org/10.1142/S0129167X03001831
  • J. Kock, Frobenius algebras and 2-d topological quantum field theories, London Mathematical Society Student Texts, no. 59, Cambridge University Press, Cambridge, 2003.
  • J. Lurie, On the classification of topological field theories, 2009. http://arXiv.org/ abs/0905.0465
  • G. W. Moore and G. Segal, D-branes and k-theory in 2d topological field theory, 2006.
  • Timothy Porter and Vladimir Turaev, Formal homotopy quantum field theories. I. Formal maps and crossed $\scr C$-algebras, J. Homotopy Relat. Struct. 3 (2008), no. 1, 113–159. MR 2426178
  • Gonçalo Rodrigues, Homotopy quantum field theories and the homotopy cobordism category in dimension $1+1$, J. Knot Theory Ramifications 12 (2003), no. 3, 287–319. MR 1983087, DOI https://doi.org/10.1142/S0218216503002548
  • V. G. Turaev, Quantum invariants of knots and 3-manifolds, De Gruyter Studies in Mathematics, vol. 18, Walter de Gruyter & Co., Berlin, 1994. MR 1292673
  • ---, Homotopy field theory in dimension $2$ and group-algebras, arXiv.org:math/9910010, 1999.
  • ---, 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
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.