On local rigidity of partially hyperbolic affine Z(k) actions

• The following dichotomy for affine Z(k) actions on the torus T-d, k, d is an element of N, is shown to hold: (i) The linear part of the action has no rank-one factors, and then the affine action is locally rigid. (ii) The linear part of the action has a rank-one factor, and then the affine action is locally rigid in a probabilistic sense if and only if the rank-one factors are trivial. Local rigidity in a probabilistic sense means that rigidity holds for a set of full measure of translation vectors in the rank-one factors.

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NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

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