T. Kobayashi and S. Nasrin,
Deformation of properly discontinuous actions of Zk on Rk+1,
Internat. J. Math. 17 (2006), no. 10, 1175-1193, math.DG/0603318..
We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations.

A distinguished feature here is that even a 'small' deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of discontinuous groups, we introduce the concepts from a group theoretic perspective, and focus on 'stability' and 'local rigidity' of discontinuous groups.

As a test case, we give an explicit description of the deformation space of Zk acting properly discontinuously on Rk+1 by affine nilpotent transformations.

Our method uses an idea of 'continuous analogue' and relies on the criterion of proper actions on nilmanifolds.

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The original publication is available at www.worldscinet.com.

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