Persistence modules with operators in Morse and Floer theory
Symplectic Geometry
2017-03-07 v1 Algebraic Topology
Dynamical Systems
Abstract
We introduce a new notion of persistence modules endowed with operators. It encapsulates the additional structure on Floer-type persistence modules coming from the intersection product with classes in the ambient (quantum) homology, along with a few other geometric situations. We provide sample applications to the -geometry of Morse functions and to Hofer's geometry of Hamiltonian diffeomorphisms, that go beyond spectral invariants and traditional persistent homology.
Cite
@article{arxiv.1703.01392,
title = {Persistence modules with operators in Morse and Floer theory},
author = {Leonid Polterovich and Egor Shelukhin and Vukašin Stojisavljević},
journal= {arXiv preprint arXiv:1703.01392},
year = {2017}
}
Comments
31 pages, 4 figures