Journal of Modern Dynamics (JMD)

On the rigidity of Weyl chamber flows and Schur multipliers as topological groups

Pages: 25 - 49, Volume 9, 2015      doi:10.3934/jmd.2015.9.25

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Kurt Vinhage - Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States (email)

Abstract: We effectively conclude the local rigidity program for generic restrictions of partially hyperbolic Weyl chamber flows. Our methods replace and extend previous ones by circumventing computations made in Schur multipliers. Instead, we construct a natural topology on $H_2(G,\mathbb{Z})$, and rely on classical Lie structure theory for central extensions.

Keywords:  Local rigidity, group actions, Schur multiplier, cocycles, partial hyperbolicity, homogeneous flows.
Mathematics Subject Classification:  Primary: 37C85; Secondary: 19C09.

Received: June 2014;      Revised: November 2014;      Available Online: May 2015.