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.
|Number of pages||30|
|Journal||Moscow Mathematical Journal|
|State||Published - 1 Oct 2017|
- Floer homology
- Hamiltonian diffeomorphism
- Persistence module
- Symplectic manifold