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Moscow Mathematical Journal, 2017, Volume 17, Number 4, Pages 757–786
DOI: https://doi.org/10.17323/1609-4514-2017-17-4-757-786 (Mi mmj657) 		 
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
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DOI: https://doi.org/10.17323/1609-4514-2017-17-4-757-786
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.
Bibliographic databases:
Document Type: Article
MSC: Primary 53D40; Secondary 58E05
Language: English
Citation: Leonid Polterovich, Egor Shelukhin, Vukašin Stojisavljević, “Persistence modules with operators in Morse and Floer theory”, Mosc. Math. J., 17:4 (2017), 757–786
Citation in format AMSBIB
\Bibitem{PolSheSto17}
\by Leonid~Polterovich, Egor~Shelukhin, Vuka{\v s}in~Stojisavljevi\'c
\paper Persistence modules with operators in Morse and Floer theory
\jour Mosc. Math.~J.
\yr 2017
\vol 17
\issue 4
\pages 757--786
\mathnet{http://mi.mathnet.ru/mmj657}
\crossref{https://doi.org/10.17323/1609-4514-2017-17-4-757-786}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000416897600010}
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    • This publication is cited in the following 20 articles:
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