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Perturbed Gradient Flow Trees and A8-algebra Structures in Morse Cohomology
ISBN-13:
9783319765846
Veröffentl:
2018
Seiten:
171
Autor:
Stephan Mescher
Serie:
6, Atlantis Studies in Dynamical Systems
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
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 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.
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 A8-relations.- 7. A8-bimodule structures on Morse chain complexes.- A. Orientations and sign computations for perturbed Morse ribbon trees.
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