Contracting extensions and contractible groups

Contractible groups and linear dilatation structures

A dilatation structure on a metric space, is a notion in between a group and a differential structure. The basic objects of a dilatation structure are dilatations (or contractions). The axioms of a dilatation structure set the rules of interaction between different dilatations. There are two notions of linearity associated to dilatation structures: the linearity of a function between two dilata...

On component extensions locally compact abelian groups

Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...

Unipotent groups and some A1-contractible smooth schemes

A Fractal Non-Contracting Class of Automata Groups

Contractible Open 3-manifolds with Free Covering Translation Groups

This paper concerns the class of contractible open 3-manifolds which are “locally finite strong end sums” of eventually end-irreducible Whitehead manifolds. It is shown that whenever a 3-manifold in this class is a covering space of another 3-manifold the group of covering translations must be a free group. It follows that such a 3-manifold cannot cover a closed 3-manifold. For each countable f...