On closed subgroups of the group of homeomorphisms of a manifold

Free products and the algebraic structure of diffeomorphism groups

Let M be a compact one–manifold. We prove that the class of finitely generated subgroups of the group Diff1`bv ` pMq, the group of C1 orientation preserving diffeomorphisms of M whose first derivatives have bounded variation, is not closed under taking finite free products. As a corollary, we show that the class of finitely generated subgroups of DiffkpMq, the group of Ck diffeomorphisms of M, ...

On bD-Sets and Associated Separation Axioms

ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE

A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...

Self-homeomorphisms of 4-manifolds with fundamental group Z

In this paper we study the classification of self-homeomorphisms of closed, connected, oriented 4-manifolds with infinite cyclic fundamental group up to pseudoisotopy, or equivalently up to homotopy. We find that for manifolds with even intersection form homeomorphisms are classified up to pseudoisotopy by their action on π1, π2 and the set of spin structures on the manifold. For manifolds with...

On category of co-coverings

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.