Perturbed Gradient Flow Trees and A¿-algebra Structures in Morse Cohomology
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ISBN-13:
9783030095260
Veröffentl:
2018
Einband:
Paperback
Erscheinungsdatum:
19.12.2018
Seiten:
200
Autor:
Stephan Mescher
Gewicht:
312 g
Format:
235x155x12 mm
Serie:
6, Atlantis Studies in Dynamical Systems
Sprache:
Englisch
Beschreibung:
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. Fukayäs 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.
Introduces a self-contained discussion of an aspect of Morse theory that has remained largely overlooked
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.
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