Geometric lattice actions, entropy and fundamental groups |
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| Authors: | D Fisher R J Zimmer |
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| Institution: | Department of Mathematics, Yale University, PO Box 208283, New Haven, CT 06520-8283, USA,? e-mail: david.fisher@yale.edu, US
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA, US
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| Abstract: | Let be a lattice in a noncompact simple Lie Group G, where . Suppose acts analytically and ergodically on a compact manifold M preserving a unimodular rigid geometric structure (e.g. a connection and a volume). We show that either the action is isometric or there exists a "large image" linear representation of . Under an additional assumption on the dynamics of the action, we associate to a virtual arithmetic quotient of full entropy.
Received: December 14, 2000 |
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| Keywords: | , Lattices in Lie groups, rigidity, rigid geometric structures, entropy, |
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