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Electronic Research Announcements

ISSN 1079-6762



Twisted cocycles and rigidity problems

Author: A. Kononenko
Journal: Electron. Res. Announc. Amer. Math. Soc. 1 (1995), 26-34
MSC (1991): Primary 58
MathSciNet review: 1336697
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Abstract: We consider a class of cohomologies associated to a group action, outline a duality method for their calculation, and apply it to study different questions related to the group action. In particular, we prove a number of results on infinitesimal and cohomological rigidity of higher rank cocompact lattice actions on imaginary boundaries of some symmetric spaces (as well as results on cohomologies of some partially hyperbolic actions and lattice actions on a broader class of homogeneous spaces). We also obtain a very transparent proof of local $C^3$ rigidity of projective actions of cocompact lattices in $PSL(2,\Bbb {R})$.

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Additional Information

A. Kononenko

Received by editor(s): February 8, 1995
Received by editor(s) in revised form: March 8, 1995
Communicated by: Svetlana Katok
Article copyright: © Copyright 1995 American Mathematical Society