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arXiv · 1703.01392

Persistence modules with operators in Morse and Floer theory

Leonid Polterovich·Egor Shelukhin·Vukašin Stojisavljević
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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 $C^0$-geometry of Morse functions and to Hofer's geometry of Hamiltonian diffeomorphisms, that go beyond spectral invariants and traditional persistent homology.

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Leonid Polterovich, Egor Shelukhin, Vukašin Stojisavljević. 2017-03-04. Persistence modules with operators in Morse and Floer theory. https://arxiv.org/abs/1703.01392

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