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Fukaya Categories and Picard–Lefschetz Theory
Zurich Lectures in Advanced Mathematics

Paul Seidel (Massachusetts Institute of Technology, Cambridge, USA)

Fukaya Categories and Picard–Lefschetz Theory

ISBN print 978-3-03719-063-0, ISBN online 978-3-03719-563-5
DOI 10.4171/063
June 2008, 334 pages, softcover, 17.0 x 24.0 cm.
46.00 Euro

The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra.

Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations, and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry.

Winner 2010 AMS Veblen Prize in Geometry

Keywords: Floer homology, Fukaya category, homological algebra, Lagrangian submanifolds, Lefschetz fibrations, mirror symmetry, pseudo-holomorphic curve, symplectic geometry

Further Information

Review in Bull. Amer. Math. Soc. 47 (2010), 735–742

Review in Zentralblatt MATH 1159.53001

Review in MR 2441780 (2009f:53143)

Colding, Seidel win 2010 AMS Veblen Prize in Geometry