Isotopy-invariant topological measures on closed orientable surfaces of higher genus

Simple item page
dc.creatorZapolsky, Frol
dc.date2009-03-15
dc.date.accessioned2026-07-07T12:52:47Z
dc.date.available2026-07-07T12:52:47Z
dc.descriptionGiven a closed orientable surface (Σ) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (Σ) and the convex compact set of additive functions on the set of isotopy classes of certain subsurfaces of (Σ). We then construct such additive functions, and thus isotopy-invariant topological measures, from probability measures on (Σ) together with some additional data. The map associating topological measures to probability measures is affine and continuous. Certain Dirac measures map to simple topological measures, while the topological measures due to Py and Rosenberg arise from the normalized Euler characteristic.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/0903.2659
dc.identifierhttp://arxiv.org/abs/0903.2659
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223411
dc.subjectGeneral Topology
dc.subjectFunctional Analysis
dc.subject28C15; 57M50
dc.titleIsotopy-invariant topological measures on closed orientable surfaces of higher genus
dc.typetext

Files

Collections

arXiv