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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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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?)

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
D. Cox and S. Katz, ``Mirror symmetry and algebraic geometry.'' Math. Surveys Monogr. 68, Amer. Math. Soc., Providence, RI, 1999. MR 1677117
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 1397274
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
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 1648082
B. Dubrovin and Y. Zhang, Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation, Commun. Math. Phys. 198 (1998), 311-361. MR 1672512
T. Eguchi, K. Hori and C. S. Xiong, Quantum cohomology and Virasoro algebra, Phys. Lett. B402 (1997), 71-80. MR 1454328
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 1492534
A. B. Givental, On the WDVV-equation in quantum K-theory,
M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. MR 0809718
J. Harris and I. Morrison. ``Moduli of curves.'' Graduate Texts in Mathematics 187, Springer, New York, 1998. MR 1631825
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 1461570
Y. Ruan, Topological sigma model and Donaldson-type invariants in Gromov theory, Duke Math. J. 83 (1996), no. 2, 461-500. MR 1390655
K. Saito, Period mapping associated to a primitive form, Publ. Res. Inst. Math. Sci. 19 (1983), 1231-1264. MR 0723468
E. Witten, Two dimensional gravity and intersection theory on moduli space, Surveys in Differential Geom. 1 (1991), 243-310. MR 1144529

Review Information:

Reviewer: Ezra Getzler
Affiliation: Northwestern University
Journal: Bull. Amer. Math. Soc. 38 (2001), 101-108
Published electronically: October 2, 2000
Review copyright: © Copyright 2000 American Mathematical Society