عنوان

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

شابک

3319765833

شابک

3319765841

شابک

9783319765839

شابک

9783319765846

شابک اشتباه

9783319765839

عنوان اصلي

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

نام عام مواد

[Book]

نام نخستين پديدآور

by Stephan Mescher.

محل نشرو پخش و غیره

Cham :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

2018.

نام خاص و کميت اثر

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

ساير جزييات

online resource

عنوان فروست

Atlantis Studies in Dynamical Systems ;

مشخصه جلد

6

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

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.

بدون عنوان

0

متن يادداشت

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.

شماره استاندارد بين المللي کتاب و موسيقي

9783319765839

موضوع مستند نشده

Complex manifolds.

موضوع مستند نشده

Dynamics.

موضوع مستند نشده

Ergodic theory.

موضوع مستند نشده

Global analysis (Mathematics)

موضوع مستند نشده

Manifolds (Mathematics)

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Complex manifolds.

موضوع مستند نشده

Dynamics.

موضوع مستند نشده

Ergodic theory.

موضوع مستند نشده

Global analysis (Mathematics)

موضوع مستند نشده

Manifolds (Mathematics)

موضوع مستند نشده

MATHEMATICS-- Topology.

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

MAT-- 038000

موضوع مستند نشده

PBKS

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Mescher, Stephan.

تاريخ عمليات

20200823111140.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y