E-Book, Englisch, Band 6, 171 Seiten
Mescher Perturbed Gradient Flow Trees and A8-algebra Structures in Morse Cohomology
1. Auflage 2018
ISBN: 978-3-319-76584-6
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 6, 171 Seiten
Reihe: Atlantis Studies in Dynamical Systems
ISBN: 978-3-319-76584-6
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
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.
