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Book Review

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Book Information:

Author: Yuri I. Manin
Title: Frobenius manifolds, quantum cohomology, and moduli spaces
Additional book information: Amer. Math. Soc., Providence, RI, 1999, xiii + 303 pp., ISBN 0-8218-1917-8, $55.00

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

  • 1. K. Behrend, Algebraic Gromov-Witten invariants. ``New trends in algebraic geometry (Warwick, 1996),'' London Math. Soc. Lecture Note Ser. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 19-70. CMP 2000:02
  • 2. D. Cox and S. Katz, ``Mirror symmetry and algebraic geometry.'' Math. Surveys Monogr. 68, Amer. Math. Soc., Providence, RI, 1999. MR 2000d:14048
  • 3. B. Dubrovin, Geometry of $2$D topological field theories. ``Integrable systems and quantum groups (Montecatini Terme, 1993),'' Lecture Notes in Math. 1620, Springer, Berlin, 1996, pp. 120-348. MR 97d:58038
  • 4. B. Dubrovin, Painlevé transcendents in two-dimensional topological field theory. ``The Painlevé property,'' CRM Ser. Math. Phys., Springer, New York, 1999, 287-412. CMP 2000:02
  • 5. B. Dubrovin, Geometry and analytic theory of Frobenius manifolds. ``Proceedings of the International Congress of Mathematicians, (Berlin, 1998),'' Doc. Math. 1998, Extra Vol. II, pp. 315-326. MR 99j:32025
  • 6. B. Dubrovin and Y. Zhang, Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation, Commun. Math. Phys. 198 (1998), 311-361. MR 2000e:53100
  • 7. T. Eguchi, K. Hori and C. S. Xiong, Quantum cohomology and Virasoro algebra, Phys. Lett. B402 (1997), 71-80. MR 98j:14035
  • 8. W. Fulton and R. Pandharipande, Notes on stable maps and quantum cohomology. ``Algebraic geometry--Santa Cruz 1995,'' Proc. Sympos. Pure Math. 62, Part 2, Amer. Math. Soc., Providence, RI, 1997, pp. 45-96. MR 98m:14025
  • 9. A. B. Givental, On the WDVV-equation in quantum K-theory, arXiv.org/abs/math/0003158.
  • 10. M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. MR 87j:53053
  • 11. J. Harris and I. Morrison. ``Moduli of curves.'' Graduate Texts in Mathematics 187, Springer, New York, 1998. MR 99g:14031
  • 12. N. Hitchin, Frobenius manifolds. ``Gauge theory and symplectic geometry (Montreal, 1995),'' NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 488, Kluwer, Dordrecht, 1997, 69-112. MR 98f:58048
  • 13. Y. Ruan, Topological sigma model and Donaldson-type invariants in Gromov theory, Duke Math. J. 83 (1996), no. 2, 461-500. MR 97d:58042
  • 14. K. Saito, Period mapping associated to a primitive form, Publ. Res. Inst. Math. Sci. 19 (1983), 1231-1264. MR 85h:32034
  • 15. E. Witten, Two dimensional gravity and intersection theory on moduli space, Surveys in Differential Geom. 1 (1991), 243-310. MR 93e:32028

Review Information:

Reviewer: Ezra Getzler
Affiliation: Northwestern University
Email: getzler@math.northwestern.edu
Journal: Bull. Amer. Math. Soc. 38 (2001), 101-108
MSC (2000): Primary 14N35, 53D45
Published electronically: October 2, 2000
Review copyright: © Copyright 2000 American Mathematical Society
American Mathematical Society