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Commuting involutions whose fixed point set consists of two special components

Pedro L. Q. Pergher, Rogério de Oliveira (2008)

Fundamenta Mathematicae

Let Fⁿ be a connected, smooth and closed n-dimensional manifold. We call Fⁿ a manifold with property when it has the following property: if N m is any smooth closed m-dimensional manifold with m > n and T : N m N m is a smooth involution whose fixed point set is Fⁿ, then m = 2n. Examples of manifolds with this property are: the real, complex and quaternionic even-dimensional projective spaces R P 2 n , C P 2 n and H P 2 n , and the connected sum of R P 2 n and any number of copies of Sⁿ × Sⁿ, where Sⁿ is the n-sphere and n is not...

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.

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