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

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...

Full description

Saved in:
Bibliographic Details
Main Author: Mescher, Stephan (Author)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing, 2018.
Edition:1st ed. 2018.
Series:Atlantis Studies in Dynamical Systems ; 6
Subjects:
Global analysis (Mathematics).
Manifolds (Mathematics).
Dynamics.
Ergodic theory.
Complex manifolds.
ISBN:9783319765846
Online Access: Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
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.

Similar Items