Details
Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology
Atlantis Studies in Dynamical Systems, Band 6
|
69,54 € |
|
| Verlag: | Springer |
| Format: | |
| Veröffentl.: | 25.04.2018 |
| ISBN/EAN: | 9783319765846 |
| Sprache: | englisch |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
<div><div>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.</div><div><br></div><div>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 beof interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.</div></div><div><br></div>
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.
<div>Dr. Stephan Mescher is a Research Fellow at the University of Leipzig. He graduated with a degree in Mathematics from Bielefeld University in 2008 and obtained his Ph.D. at the University of Leipzig in 2017, supervised by Prof. Matthias Schwarz.</div>
<div>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.</div><div><br></div><div>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.</div>
Introduces a self-contained discussion of an aspect of Morse theory that has remained largely overlooked Includes an accessible introduction to a part of Morse theory that is closely related to algebraic topology Offers a useful preparation for the study of Fukaya categories in Lagrangian Floer theory
Diese Produkte könnten Sie auch interessieren:
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
von: Kenneth Meyer, Glen Hall, Dan Offin
106,99 €
