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Twisted Cocycles and Rigidity Problems.
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## Twisted cocycles and rigidity problems

### A. Kononenko

**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 $PSL(2,\Bbb{R})$.

*Copyright American Mathematical Society 1995 *

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**Article Info**
- ERA Amer. Math. Soc.
**01** (1995), pp. 26-34
- Publisher Identifier: S 1079-6762(95)01004-0
- 1991
*Mathematics Subject Classification*. 58.
- Received by the editors February 8, 1995, and, in revised form, March 8, 1995
- Communicated by Svetlana Katok
- Comments (When Available)

**A. Kononenko**

Department of Mathematics, Pennsylvania State University,
218 McAllister Building, University Park, PA 16802.

*E-mail address:* `avk@math.psu.edu`

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