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˚-geometry of Morse functions and to Hofer’s geometry of Hamiltonian diffeomorphisms that go beyond spectral invariants and traditional persistent homology.
Original language | English |
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Pages (from-to) | 757-786 |
Number of pages | 30 |
Journal | Moscow Mathematical Journal |
Volume | 17 |
Issue number | 4 |
DOIs | |
State | Published - 1 Oct 2017 |
Keywords
- Barcode
- Floer homology
- Hamiltonian diffeomorphism
- Persistence module
- Symplectic manifold