In which paper did J. F. Plante introduce (for the first time) the notion of Holonomy Invariant Transverse Measure?
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Thanks in Advance.
2026-03-25 19:32:49.1774467169
In which paper did J. F. Plante introduce the notion of Holonomy Invariant Transverse Measure?
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Without attributing ownership to Plante (because it seems to me this requires a historical study ($\dagger$)), probably the paper is "Foliations with Measure Preserving Holonomy", published in 1975. It seems in the literature it is common to cite this paper as well as Ruelle & Sullivan's 1975 paper "Currents, Flows and Diffeomorphisms". Garnett's 1981 PhD thesis Functions and measures harmonic along the leaves of a foliation and the ergodic theorem (available at https://doi.org/10.1349/ddlp.1154) seems like a useful source in this context.
($\dagger$) E.g. Schwartzman and Sacksteder's papers are also mentioned at times.