Book Review

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Book Information:

Author: Paul Seidel

Title: Fukaya categories and Picard-Lefschetz theory

Additional book information: European Mathematical Society (EMS), Zürich, 2008, vii+326 pp., ISBN 978-3-03719-063-0, {\EUR {46}}

**[Arn95]**V. I. Arnol'd. ``Some remarks on symplectic monodromy of Milnor fibrations'', in*The Floer Memorial Volume*, (Hofer, Taubes, Weinstein, Zehnder, eds.). Birkhäuser, 1995. MR**1362824 (96m:32043)****[Flo88]**A. Floer.*Morse theory for Lagrangian intersections.*J. Diff. Geom. 28:513-547 (1988). MR**965228 (90f:58058)****[FO3]**K. Fukaya, Y.-G. Oh, H. Ohta, and K. Ono.*Lagrangian intersection Floer theory: anomaly and obstruction.*AMS/IP Studies in Advanced Mathematics, 46.1. American Mathematical Society, Providence, RI, and International Press, Somerville, MA, 2009.**[Gr85]**M. Gromov.*Pseudoholomorphic curves in symplectic manifolds.*Invent. Math. 82:307-47 (1985). MR**809718 (87j:53053)****[HV00]**K. Hori and C. Vafa.*Mirror symmetry.*Preprint,`arXiv:hep-th/0002222`.**[Kon95]**M. Kontsevich.*Homological algebra of mirror symmetry.*Proceedings of the International Congress of Mathematicians, Zurich, 1994. Birkhäuser, 1995. MR**1403918 (97f:32040)****[La81]**K. Lamotke.*The topology of complex projective varieties after S. Lefschetz.*Topology 20:15-51 (1981). MR**592569 (81m:14019)****[MOS]**C. Manolescu, P. Ozsváth and S. Sarkar.*A combinatorial description of knot Floer homology.*Ann. of Math. 169:663-660 (2009). MR**2480614 (2009k:57047)****[Mil69]**J. Milnor.*Morse theory.*Princeton University Press, 1969. MR**0163331 (29:634)****[OS04]**P. Ozsváth and Z. Szabó.*Holomorphic disks and topological invariants for closed three-manifolds.*Ann. of Math. 159:1027-1158 (2004). MR**2113019 (2006b:57016)****[Sei02]**P. Seidel. ``Fukaya categories and deformations'', in*Proceedings of the International Congress of Mathematicians*(Beijing, 2002). Higher Ed. Press, 2002. MR**1957046 (2004a:53110)****[Sei03]**P. Seidel.*Homological mirror symmetry for the quartic surface.*Preprint,`arXiv:math.SG/0310414`.**[Sei08]**P. Seidel.*Homological mirror symmetry for the genus two curve.*Preprint,`arXiv:0812.1171`.

Review Information:

Reviewer: Ivan Smith

Affiliation: Cambridge, United Kingdom

Email: is200@cam.ac.uk

Journal: Bull. Amer. Math. Soc.

**47**(2010), 735-742

MSC (2000): Primary 53D37, 53D40

DOI: https://doi.org/10.1090/S0273-0979-10-01289-9

Published electronically: February 24, 2010

Review copyright: © Copyright 2010 American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.