Perturbed Gradient Flow Trees and A -algebra Structures in Morse Cohomology Paperback / softback
by Stephan Mescher
Part of the Atlantis Studies in Dynamical Systems series
Paperback / softback
Description
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 beof interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.
Information
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Item not Available
- Format:Paperback / softback
- Pages:171 pages, 20 Illustrations, black and white; XXV, 171 p. 20 illus.
- Publisher:Springer Nature Switzerland AG
- Publication Date:19/12/2018
- Category:
- ISBN:9783030095260
Information
-
Item not Available
- Format:Paperback / softback
- Pages:171 pages, 20 Illustrations, black and white; XXV, 171 p. 20 illus.
- Publisher:Springer Nature Switzerland AG
- Publication Date:19/12/2018
- Category:
- ISBN:9783030095260
