Book Review
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MathSciNet review:
2919689
Full text of 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
Mark Brightwell and Paul Turner, Representations of the homotopy surface category of a simply connected space, J. Knot Theory Ramifications 9 (2000), no. 7, 855–864. MR 1780591, DOI 10.1142/S0218216500000487
M. Fukuma, S. Hosono, and H. Kawai, Lattice topological field theory in two dimensions, Comm. Math. Phys. 161 (1994), no. 1, 157–175. MR 1266073
Ralph M. Kaufmann, Orbifolding Frobenius algebras, Internat. J. Math. 14 (2003), no. 6, 573–617. MR 1997832, DOI 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 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.
References
- 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)
- 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)
- R. M. Kaufmann, Orbifolding Frobenius algebras, Int. J. Math. 14 (2003), no. 6, 573–617. MR 1997832 (2005b:57057)
- 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.
- 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)
- 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)
- 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)
- —, 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.
