Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology (Atlantis Studies in Dynamical Systems, 6) - Softcover

Mescher, Stephan

Softcover

ISBN 10: 3030095266 ISBN 13: 9783030095260

Publisher: Springer, 2018

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 be of interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.

About this title

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.

Edition details

• Publisher: Springer
• Publication date: 2018
• ISBN 10: 3030095266
• ISBN 13: 9783030095260
• Binding: Paperback
• Language: English
• Number of pages: 196