The subject of Fukaya categories has a reputation for being hard to approach. This is due to the amount of background knowledge required taken from homological algebra, symplectic geometry, and geometric analysis , and equally to the rather complicated nature of the basic definitions. The present book is intended as a resource for graduate students and researchers whowould like to learn about Fukaya categories, and possibly use them in their own work. I have tried to focus on a rather basic subset of topics, and to describe these as precisely as I could, filling in gaps found in some of the early references. This makes for a rather austere style for that reason, a thorough study of this book should probably be complemented by reading some of the papers dealing with applications.
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Moogusar Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations and contains many previously unpublished results. Yes, I have that as well as some other references in my que.
In addition, any references with an eye toward homological mirror symmetry would be greatly fukaa. The picard-lefschtez topic of this book is a construction of a Fukaya category, an object capturing information on Lagrangian submanifolds of a given symplectic manifold. The last part treats Lefschetz fibrations and their Fukaya categories and briefly illustrates the theory on the example of Am-type Milnor fibres. European Mathematical Society- Mathematics — pages.
Identity morphisms and equivalences. I am asking if anyone personally recommends references that they have read on the subject that they find to be good introductions especially for self-studyin order to whittle down the references I have to a few good ones.
The Fukaya category of a Lefschetz fibration. The Fukaya category preliminary version. Fukaya Categories and Picard—Lefschetz Theory. Post as a guest Name. A little symplectic geometry. Read, highlight, and take notes, across web, tablet, and phone. A google search yielded this: The last part discusses applications to Lefschetz fibrations and contains many previously unpublished results.
Print Price 2 Label: Well, I do try to have a geometric understanding of anything I can… but I personally gravitate more towards anything higher category-theortic, so I suppose it would be the latter. Fukaya Categories and Picard-Lefschetz Theory The main topic of this book is a construction of a Fukaya category, an object capturing information on Lagrangian submanifolds of a given symplectic manifold.
Fukaya categories are of interest due to the recent formulation of homological mirror symmetry. Fukaya Categories Ask Question. The reader is expected to have a certain background in symplectic geometry.
The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry. Another good reference is the paper http: Indices and determinant lines. Sign up using Facebook. Email Pjcard-lefschetz, but never shown. A publication of the European Mathematical Society. Skip to main content. Sign up using Email and Password.
Ordering on the AMS Bookstore is limited to individuals for personal use only. Generally, the emphasis is on simplicity rather than generality. The relevant aspects of pseudo-holomorphic curve categorie are covered in some detail, and there is also a self-contained account of the necessary homological algebra. TOP Related Posts.
FUKAYA CATEGORIES AND PICARD-LEFSCHETZ THEORY PDF
Fejar The Fukaya category complete version. A little symplectic geometry. A google search yielded this: Selected pages Title Page. A publication of the European Mathematical Society.
Fukaya Categories and Picard-Lefschetz Theory