Tropical Fukaya algebras / Sushmita Venugopalan, Chris T. Woodward.

Format:

Book

Author/Creator:

Venugopalan, Sushmita, author.

Woodward, Chris T. (Christopher Thomas), author.

Series:

EMS monographs in mathematics

EMS monographs in Mathematics

Language:

English

Subjects (All):

Floer homology.

Symplectic geometry.

Tropical geometry.

Physical Description:

ix, 367 pages : illustrations, some color ; 24 cm.

Place of Publication:

Berlin: , EMS Press, [2025]

Summary:

"In this book, the authors explore the degeneration of pseudoholomorphic disks bounding a Lagrangian in a symplectic manifold in the large complex structure limit corresponding to a multiple cut. The limit objects, called broken disks, have underlying tropical graphs, which in the case of pseudoholomorphic spheres were studied by Brett Parker. In particular, the authors study the limit of the Fukaya algebra of a Lagrangian submanifold, which is an A ∞ algebra whose higher composition maps involve counts of pseudoholomorphic disks. The goal of the book is to prove an A ∞ homotopy equivalence between the ordinary Fukaya algebra of a Lagrangian and a tropical version of the Fukaya algebra defined via counts of broken disks with rigid tropical graphs.The exposition is self-contained and includes details of the transversality scheme. Various computations of disk potentials of Lagrangian submanifolds, such as those in cubic surfaces and flag varieties, are included."--Back cover.

Contents:

Statement of results

Applications to disk counting

Broken manifolds

Broken disks

Stabilizing divisors

Coherent perturbations and regularity

Hofer energy and exponential decay

Gromov compactness

Gluing

Broken Fukaya algebras

Potentials for semi-Fano toric surfaces.

Notes:

Includes bibliographical references (pages 359-363) and index.

Other Format:

Online version: Venugopalan, Sushmita. Tropical Fukaya algebras.

ISBN:

9783985470938

3985470936

OCLC:

1540953200