Birational equivalence in the symplectic category.
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.
In [R] explicit representatives for -principal bundles over are constructed, based on these constructions explicit free -actions on the total spaces are described, with quotients exotic -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 -spheres that occur as quotients of the free -actions described above.