Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology

• Main Author: Mescher, Stephan (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Atlantis Studies in Dynamical Systems ; 6
• Subjects: Global analysis (Mathematics).; Manifolds (Mathematics).; Dynamics.; Ergodic theory.; Complex manifolds.; Global Analysis and Analysis on Manifolds.; Dynamical Systems and Ergodic Theory.; Manifolds and Cell Complexes (incl. Diff.Topology).

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...

Table of Contents:

• 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.