Perturbed Gradient Flow Trees and A -algebra Structures in Morse Cohomology
(Sprache: Englisch)
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...
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Klappentext zu „Perturbed Gradient Flow Trees and A -algebra Structures in Morse Cohomology “
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.
Inhaltsverzeichnis zu „Perturbed Gradient Flow Trees and A -algebra Structures in Morse Cohomology “
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.
Autoren-Porträt von Stephan Mescher
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.
Bibliographische Angaben
- Autor: Stephan Mescher
- 2018, Softcover reprint of the original 1st ed. 2018, XXV, 171 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3030095266
- ISBN-13: 9783030095260
Sprache:
Englisch
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