JournalscmhVol. 91, No. 1pp. 39–64

Livšic theorem for low-dimensional diffeomorphism cocycles

  • Alejandro Kocsard

    Universidade Federal Fluminense, Niterói, Brazil

  • Rafael Potrie

    Universidad de la República, Montevideo, Uruguay
Livšic theorem for low-dimensional diffeomorphism cocycles cover
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Abstract

We prove a Livšic type theorem for cocycles taking values in groups of diffeomorphisms of low-dimensional manifolds. The results hold without any localization assumption and in very low regularity. We also obtain a general result (in any dimension) which gives necessary and sufficient conditions to be a coboundary.

Cite this article

Alejandro Kocsard, Rafael Potrie, Livšic theorem for low-dimensional diffeomorphism cocycles. Comment. Math. Helv. 91 (2016), no. 1, pp. 39–64

DOI 10.4171/CMH/377