https://univ-artois.hal.science/hal-03661140Prieto, José Ignacio RoyoJosé Ignacio RoyoPrietoUPV/EHU - Universidad del Pais Vasco / Euskal Herriko Unibertsitatea [Espagne]Saralegi-Aranguren, MartintxoMartintxoSaralegi-ArangurenLML - Laboratoire de Mathématiques de Lens - UA - Université d'ArtoisWolak, RobertRobertWolakInstitute of Mathematics Jagiellonian University - UJ - Uniwersytet Jagielloński w Krakowie = Jagiellonian UniversityHard Lefschetz Property for Isometric FlowsHAL CCSD2022[MATH.MATH-AT] Mathematics [math]/Algebraic Topology [math.AT]Saralegi-Aranguren, Martintxo2022-05-06 15:50:072023-09-20 15:36:052022-05-06 15:50:07enJournal articles1The Hard Lefschetz Property (HLP) is an important property which has been studied in several categories of the symplectic world. For Sasakian manifolds, this duality is satisfied by the basic cohomology (so, it is a transverse property), but a new version of the HLP has been recently given in terms of duality of the cohomology of the manifold itself in arXiv:1306.2896. Both properties were proved to be equivalent (see arXiv:1311.1431) in the case of K-contact flows. In this paper we extend both versions of the HLP (transverse and not) to the more general category of isometric flows, and show that they are equivalent. We also give some explicit examples which illustrate the categories where the HLP could be considered.