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

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Given 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.

Original languageEnglish
Pages (from-to)133-143
Number of pages11
JournalMathematische Zeitschrift
Issue number1-2
StatePublished - Feb 2012
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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