Periodic cycle functions and cocycle rigidity for certain partially hyperbolic $\mathbb R^k$ actions
Danijela Damjanović - Erwin Schroedinger Institute, Boltzmanngasse 9, A-1090 Vienna, Austria (email)
Abstract: We give a proof of cocycle rigidity in Hölder and smooth categories for Cartan actions on $SL(n, \mathbb R)$/$\Gamma$ and $SL(n, \mathbb C)$/$\Gamma$ for $n\ge 3$ and $\Gamma$ cocompact lattice, and for restrictions of those actions to subspaces which contain a two-dimensional plane in general position. This proof does not use harmonic analysis, it relies completely on the structure of stable and unstable foliations of the action. The key new ingredient is the use of the description of generating relations in the group $SL_n$.
Keywords: Cocycles, rigidity, Weyl chamber flow, partial hyperbolicity.
Received: November 2004; Revised: May 2005; Published: August 2005.
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