عنوان

Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology

(Number (ISBN

3319765833

(Number (ISBN

3319765841

(Number (ISBN

9783319765839

(Number (ISBN

9783319765846

Erroneous ISBN

9783319765839

Title Proper

Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology

General Material Designation

[Book]

First Statement of Responsibility

by Stephan Mescher.

Place of Publication, Distribution, etc.

Cham :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2018.

Specific Material Designation and Extent of Item

1 online resource (XXV, 171 pages 20 illustrations) :

Other Physical Details

online resource

Series Title

Atlantis Studies in Dynamical Systems ;

Volume Designation

6

Text of Note

Includes bibliographical references and index.

Text of Note

1. Basics on Morse homology -- 2. Perturbations of gradient flow trajectories -- 3. Nonlocal generalizations -- 4. Moduli spaces of perturbed Morse ribbon trees -- 5. The convergence behaviour of sequences of perturbed Morse ribbon trees -- 6. Higher order multiplications and the A∞-relations -- 7. A∞-bimodule structures on Morse chain complexes -- A. Orientations and sign computations for perturbed Morse ribbon trees.

0

Text of Note

This book elaborates on an idea put forward by M. Abouzaid on equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an A∞-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya's definition of Morse-A∞-categories for closed oriented manifolds involving families of Morse functions. To make A∞-structures in Morse theory accessible to a broader audience, this book provides a coherent and detailed treatment of Abouzaid's approach, including a discussion of all relevant analytic notions and results, requiring only a basic grasp of Morse theory. In particular, no advanced algebra skills are required, and the perturbation theory for Morse trajectories is completely self-contained. In addition to its relevance for finite-dimensional Morse homology, this book may be used as a preparation for the study of Fukaya categories in symplectic geometry. It will be of interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.

International Standard Book Number

9783319765839

Complex manifolds.

Dynamics.

Ergodic theory.

Global analysis (Mathematics)

Manifolds (Mathematics)

Mathematics.

Complex manifolds.

Dynamics.

Ergodic theory.

Global analysis (Mathematics)

Manifolds (Mathematics)

MATHEMATICS-- Topology.

Mathematics.

MAT-- 038000

PBKS

Number

Edition

Class number

Mescher, Stephan.

Date of Transaction

20200823111140.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y