Fukaya Categories and Picard-Lefschetz Theory 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024


Fukaya Categories and Picard-Lefschetz Theory

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Paul Seidel 作者
European Mathematical Society
譯者
2008-6-15 出版日期
334 頁數
USD 58.00 價格
Paperback
Zurich Lectures in Advanced Mathematics 叢書系列
9783037190630 圖書編碼

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Fukaya Categories and Picard-Lefschetz Theory 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024



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Fukaya Categories and Picard-Lefschetz Theory 在線電子書 著者簡介


Fukaya Categories and Picard-Lefschetz Theory 在線電子書 著者簡介


Fukaya Categories and Picard-Lefschetz Theory 在線電子書 pdf 下載 txt下載 epub 下載 mobi 在線電子書下載

Fukaya Categories and Picard-Lefschetz Theory 在線電子書 圖書描述

Preface

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). A second aim was to give an account of some previously

unpublished results, which connect Fukaya categories to the theory of Lefschetz

fibrations. This becomes predominant in the last sections, where the text gradually

turns into a research monograph.

I have borrowed liberally from the work of many people, first and foremost among

them Fukaya, Kontsevich, and Donaldson. Fukaya’s foundational contribution, of

course, was to introduce A1-structures into symplectic geometry. On the algebraic

side, he pioneered the use of the A1-version of the Yoneda embedding, which we

adopt systematically. Besides that, several geometric ideas, such as the role of Pin

structures, and the construction of A1-homomorphisms in terms of parametrized

moduli spaces, are taken from the work of Fukaya, Oh, Ohta and Ono. Kontsevich

introduced derived categories of A1-categories, and is responsible for much of

their theory, in particular the intrinsic characterization of exact triangles. He also

conjectured the relation between Dehn twist and twist functors, which is one of our

main results. Finally, in joint work with Barannikov, he suggested a construction

of Fukaya categories for Lefschetz fibrations; we use a superficially different, but

presumably equivalent, definition. Donaldson’s influence is equally pervasive. Besides

his groundbreaking work on Lefschetz pencils, he introduced matching cycles,

and proposed them as the starting point for a combinatorial formula for Floer cohomology,

which is indeed partly realized here. Other mathematicians have also made

important contributions. For instance, parts of our presentation of Picard–Lefschetz

theory reflect Auroux’ point of view. A result of Smith, namely that the vanishing

cycles in a four-dimensional Lefschetz pencil necessarily fill out the fibre, was crucial

in suggesting that such cycles might “split-generate” the Fukaya category. Besides

that, work of Fukaya–Smith on cotangent bundles provided a good testing-ground

for some of the more adventurous ideas about Lefschetz fibrations. Our approach

to transversality issues is the result of several conversations with Lazzarini. Finally,

Abouzaid’s suggestions greatly improved the discussion of symplectic embeddings.

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Fukaya Categories and Picard-Lefschetz Theory 在線電子書 讀後感

評分

由于in general定义Lagrangian Floer theory存在obstruction,因此本书讨论了exact symplectic manifold (with corners) [;M;]中的closed exact Lagrangian。这样做的好处是运用Stokes定理可以看出没有disc bubbling,从而这些Lagrangian submanifold tautologically unobstruc...

評分

由于in general定义Lagrangian Floer theory存在obstruction,因此本书讨论了exact symplectic manifold (with corners) [;M;]中的closed exact Lagrangian。这样做的好处是运用Stokes定理可以看出没有disc bubbling,从而这些Lagrangian submanifold tautologically unobstruc...

評分

由于in general定义Lagrangian Floer theory存在obstruction,因此本书讨论了exact symplectic manifold (with corners) [;M;]中的closed exact Lagrangian。这样做的好处是运用Stokes定理可以看出没有disc bubbling,从而这些Lagrangian submanifold tautologically unobstruc...

評分

由于in general定义Lagrangian Floer theory存在obstruction,因此本书讨论了exact symplectic manifold (with corners) [;M;]中的closed exact Lagrangian。这样做的好处是运用Stokes定理可以看出没有disc bubbling,从而这些Lagrangian submanifold tautologically unobstruc...

評分

由于in general定义Lagrangian Floer theory存在obstruction,因此本书讨论了exact symplectic manifold (with corners) [;M;]中的closed exact Lagrangian。这样做的好处是运用Stokes定理可以看出没有disc bubbling,从而这些Lagrangian submanifold tautologically unobstruc...

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