Book Review
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MathSciNet review:
2721047
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Book Information:
Author:
Paul Seidel
Title:
Fukaya categories and Picard-Lefschetz theory
Additional book information:
European Mathematical Society (EMS), Z\"{u}rich,
2008,
vii+326 pp.,
ISBN 978-3-03719-063-0,
\EUR{46}
V. I. Arnol′d, Some remarks on symplectic monodromy of Milnor fibrations, The Floer memorial volume, Progr. Math., vol. 133, Birkhäuser, Basel, 1995, pp. 99–103. MR 1362824
Andreas Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988), no. 3, 513–547. MR 965228
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.
M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347. MR 809718, DOI 10.1007/BF01388806
K. Hori and C. Vafa. Mirror symmetry. Preprint, arXiv:hep-th/0002222.
Maxim Kontsevich, Homological algebra of mirror symmetry, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994) Birkhäuser, Basel, 1995, pp. 120–139. MR 1403918
Klaus Lamotke, The topology of complex projective varieties after S. Lefschetz, Topology 20 (1981), no. 1, 15–51. MR 592569, DOI 10.1016/0040-9383(81)90013-6
Ciprian Manolescu, Peter Ozsváth, and Sucharit Sarkar, A combinatorial description of knot Floer homology, Ann. of Math. (2) 169 (2009), no. 2, 633–660. MR 2480614, DOI 10.4007/annals.2009.169.633
J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331
Peter Ozsváth and Zoltán Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. (2) 159 (2004), no. 3, 1027–1158. MR 2113019, DOI 10.4007/annals.2004.159.1027
Paul Seidel, Fukaya categories and deformations, Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002) Higher Ed. Press, Beijing, 2002, pp. 351–360. MR 1957046
P. Seidel. Homological mirror symmetry for the quartic surface. Preprint, arXiv:math.SG/0310414.
P. Seidel. Homological mirror symmetry for the genus two curve. Preprint, arXiv:0812.1171.
References
- 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)
- A. Floer. Morse theory for Lagrangian intersections. J. Diff. Geom. 28:513-547 (1988). MR 965228 (90f:58058)
- 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.
- M. Gromov. Pseudoholomorphic curves in symplectic manifolds. Invent. Math. 82:307-47 (1985). MR 809718 (87j:53053)
- K. Hori and C. Vafa. Mirror symmetry. Preprint, arXiv:hep-th/0002222.
- M. Kontsevich. Homological algebra of mirror symmetry. Proceedings of the International Congress of Mathematicians, Zurich, 1994. Birkhäuser, 1995. MR 1403918 (97f:32040)
- K. Lamotke. The topology of complex projective varieties after S. Lefschetz. Topology 20:15-51 (1981). MR 592569 (81m:14019)
- 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)
- J. Milnor. Morse theory. Princeton University Press, 1969. MR 0163331 (29:634)
- 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)
- P. Seidel. “Fukaya categories and deformations”, in Proceedings of the International Congress of Mathematicians (Beijing, 2002). Higher Ed. Press, 2002. MR 1957046 (2004a:53110)
- P. Seidel. Homological mirror symmetry for the quartic surface. Preprint, arXiv:math.SG/0310414.
- 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
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.
