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This article is cited in 20 scientific papers (total in 20 papers)
Persistence modules with operators in Morse and Floer theory
Leonid Polterovicha, Egor Shelukhinbc, Vukašin Stojisavljevića a School of Mathematical Sciences, Tel Aviv University
b IAS, Princeton
c DMS at U. of Montreal
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.
Key words and phrases:
symplectic manifold, Hamiltonian diffeomorphism, Floer homology, persistence module, barcode.
Citation:
Leonid Polterovich, Egor Shelukhin, Vukašin Stojisavljević, “Persistence modules with operators in Morse and Floer theory”, Mosc. Math. J., 17:4 (2017), 757–786
Linking options:
https://www.mathnet.ru/eng/mmj657 https://www.mathnet.ru/eng/mmj/v17/i4/p757
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Abstract page: | 214 | References: | 49 |
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