Perturbed gradient flow trees and $A_\infty$-algebra structures on Morse cochain complexes
Geometric Topology
2016-11-24 v1 Dynamical Systems
Symplectic Geometry
Abstract
We elaborate on an idea of M. Abouzaid of equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an -algebra. This is a variation on K. Fukaya's definition of Morse--categories for closed oriented manifolds involving families of Morse functions. The purpose of this article is to provide a coherent and detailed treatment of Abouzaid's approach including a discussion of all relevant analytic notions and results.
Keywords
Cite
@article{arxiv.1611.07916,
title = {Perturbed gradient flow trees and $A_\infty$-algebra structures on Morse cochain complexes},
author = {Stephan Mescher},
journal= {arXiv preprint arXiv:1611.07916},
year = {2016}
}
Comments
100 pages, 18 figures. The contents of this article are parts of the author's Ph.D. thesis, submitted to the University of Leipzig in September 2016