Perturbed Gradient Flow Trees and A¿-algebra Structures in Morse Cohomology
Stephan Mescher
ISBN 10: 3030095266 ISBN 13: 9783030095260
Published by Springer, 2018
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Perturbed Gradient Flow Trees and A¿-algebra Structures in Morse Cohomology | Stephan Mescher | Taschenbuch | xxv | Englisch | 2018 | Springer | EAN 9783030095260 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Seller Inventory # 116276096
Synopsis:
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 beof interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.
About the Author:
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.
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Bibliographic Details
Title: Perturbed Gradient Flow Trees and A¿-algebra...
Publisher: Springer
Publication Date: 2018
Binding: Taschenbuch
Condition: Neu