We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has tw...

Let G be a compact connected Lie group with maximal torus T , and H a closed subgroup containing T . We work out the Atiyah-Bott-Berline-Vergne localization formula for the homogeneous space G/H under the natural action of the maximal torus T . The computation gives explicit formulas for the ordinary and equivariant characteristic numbers of a homogeneous space. Let G be a compact connected Lie...

We prove the consistency (modulo supercompact) of a negative answer to the Cantor discontinuum partition problem (i.e., some Hausdorff compact space cannot be partitioned to two sets not containing a closed copy of Cantor discontinuum). In this model we have CH. Without CH we get consistency results using a pcf assumption, close relatives of which are necessary for such results; so we try to de...

A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known quantum homogeneous spaces are revisited. MSC: 16W35; 20G42; 17B37; 81R50