Perturbed Gradient Flow Trees and A8-algebra Structures in Morse Cohomology / Atlantis Studies in Dynamical Systems Bd.6 (PDF)
(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 A8-algebra by means of perturbed gradient flow trajectories. This approach is...
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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 A8-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya's definition of Morse-A8-categories for closed oriented manifolds involving families of Morse functions. To make A8-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.
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, 1st ed. 2018, 171 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319765841
- ISBN-13: 9783319765846
- Erscheinungsdatum: 25.04.2018
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- Größe: 2.68 MB
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Englisch
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