About: Poisson smooth structures on stratified symplectic spaces

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper we introduce the notion of a smooth structure on a stratified space, the notion of a Poisson smooth structure and the notion of a weakly symplectic smooth structure on a stratified symplectic space, refining the concept of a stratified symplectic Poisson algebra introduced by Sjamaar and Lerman. We show that these smooth spaces possess several important properties, e.g., the existence of smooth partitions of unity. Furthermore, under mild conditions many properties of a symplectic manifold can be extended to a symplectic stratified space provided with a smooth Poisson structure, e.g., the existence and uniqueness of a Hamiltonian flow, the isomorphism between the Brylinski-Poisson homology and the de Rham homology, and the existence of a Lefschetz decomposition on a symplectic stratified space. We give many examples of stratified symplectic spaces possessing a Poisson smooth structure which is also weakly symplectic. In this paper we introduce the notion of a smooth structure on a stratified space, the notion of a Poisson smooth structure and the notion of a weakly symplectic smooth structure on a stratified symplectic space, refining the concept of a stratified symplectic Poisson algebra introduced by Sjamaar and Lerman. We show that these smooth spaces possess several important properties, e.g., the existence of smooth partitions of unity. Furthermore, under mild conditions many properties of a symplectic manifold can be extended to a symplectic stratified space provided with a smooth Poisson structure, e.g., the existence and uniqueness of a Hamiltonian flow, the isomorphism between the Brylinski-Poisson homology and the de Rham homology, and the existence of a Lefschetz decomposition on a symplectic stratified space. We give many examples of stratified symplectic spaces possessing a Poisson smooth structure which is also weakly symplectic. (en)
Title	Poisson smooth structures on stratified symplectic spaces Poisson smooth structures on stratified symplectic spaces (en)
skos:prefLabel	Poisson smooth structures on stratified symplectic spaces Poisson smooth structures on stratified symplectic spaces (en)
skos:notation	RIV/67985840:_____/15:00437490!RIV15-AV0-67985840
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(IAA100190701)
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Vanžura, Jiří Le, Hong-Van
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	345
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/15:00437490
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	algebraic topology (en)
http://linked.open.../riv/klicoveSlovo	algebraic topology
http://linked.open...ontrolniKodProRIV	[73EEF8EC3096]
http://linked.open...v/mistoKonaniAkce	Lahore
http://linked.open...i/riv/mistoVydani	Basel
http://linked.open...i/riv/nazevZdroje	Mathematics in the 21st Century : 6th World Conference, Lahore, March 2013
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Investigating manifolds with special structures from topological and geometric-analytical points of view
http://linked.open...UplatneniVysledku	2015
http://linked.open...iv/tvurceVysledku	Le, Hong-Van Vanžura, Jiří Somberg, P.
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2013-03-06 (xsd:date)
issn	2194-1009
number of pages	24 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/978-3-0348-0859-0_11
http://purl.org/ne...btex#hasPublisher	Springer-Verlag
https://schema.org/isbn	978-3-0348-0858-3

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