The Projective Group as a Topological Manifold

Lattice of compactifications of a topological group

We show that the lattice of compactifications of a topological group $G$ is a complete lattice which is isomorphic to the lattice of all closed normal subgroups of the Bohr compactification $bG$ of $G$. The correspondence defines a contravariant functor from the category of topological groups to the category of complete lattices. Some properties of the compactification lattice of a topological ...

Projective Group Structures as Absolute Galois Structures

We prove: A proper profinite group structure G is projective if and only if G is the absolute Galois group structure of a proper field-valuation structure with block approximation. MR Classification: 12E30 Directory: \Jarden\Diary\HJPa 30 April, 2008 * Research supported by the Minkowski Center for Geometry at Tel Aviv University, established by the Minerva Foundation. ** Research partially don...

Free Topological Groups and the Projective Dimension of a Locally Compact Abelian Group

It is shown that a free topological group on a k.space is a k.-space. Using this it is proved that if X is a k.-group then it is a quotient of a free topological group by a free topological group. A corollary to this is that the projective dimension of any k.-group, relative to the class of all continuous epimorphisms admitting sections, is either zero or one. In particular the projective dimen...

On an Einstein Projective Sasakian Manifold

In this paper, we have proved that a projectively flat Sasakian manifold is an Einstein manifold. Also, if an Einstein-Sasakian manifold is projectively flat, then it is locally isometric with a unit sphere S(1). It has also been proved that if in an Einsten-Sasakian manifold the relation K(X, Y ).P = 0 holds, then it is locally isometric with a unit sphere S(1). AMS Mathematics Subject Classif...

Bernhard Brehm Topological Stable Manifold