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Book Information

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

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 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

Reviewer(s):
Ezra Getzler
Affiliation: Northwestern University
Email: getzler@math.northwestern.edu

MSC (2000): Primary 14N35, 53D45
DOI: 10.1090/S0273-0979-00-00888-0
PII: S 0273-0979(00)00888-0
Posted: October 2, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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