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Continuous Measures on Homogenous Spaces

Michael Björklund, Alexander Fish (2009)

Annales de l’institut Fourier

In this paper we generalize Wiener’s characterization of continuous measures to compact homogenous manifolds. In particular, we give necessary and sufficient conditions on probability measures on compact semisimple Lie groups and nilmanifolds to be continuous. The methods use only simple properties of heat kernels.

Correction for the paper “ S 3 -bundles and exotic actions”

T. E. Barros (2001)

Bulletin de la Société Mathématique de France

In [R] explicit representatives for S 3 -principal bundles over S 7 are constructed, based on these constructions explicit free S 3 -actions on the total spaces are described, with quotients exotic 7 -spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. In Theorem 1 below, we correct the classification formula and in Theorem 2 we exhibit the correct indices of the exotic 7 -spheres that occur as quotients of the free S 3 -actions described above.

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