On Geometric Simple Connectivity

L'articolo intende dare una visione panoramica su ricerche recenti, molte delle quali sono da attribuire al V.Poenaru, sulla topologia di dimensione basse e sulla teoria geometrica dei gruppi.

Some remarks on universal covers and groups

We give a quick reviw of problems concerning the topological behavior of contractible covering spaces, from the point of view of the topology at infinity.

Some remarks on Geometric simple connectivity in dimension Four. Part A

The present paper contains some complements and comments to the longer article Geometric simple connectivity in smooth four dimensional differential Topology, Part A. Its aim is to be a useful companion when reading that article,and also to help in understand how it fits into the first author’s programforthe Poincar´e conjecture.

A Group-theoretical Finiteness Theorem

We start with the universal covering space $${\*M^n}$$ of a closed n-manifold and with a tree of fundamental domains which zips it $${T\longrightarrow\*M^n}$$ . Our result is that, between T and $${\* M^n}$$ , is an intermediary object, $${T\stackrel{p} {\longrightarrow} G \stackrel{F}{\longrightarrow} \*M^n}$$ , obtained by zipping, such that each fiber of p is finite and $${T\stackrel{p}{\longrightarrow}G\stackrel{F}{\longrightarrow} \*M^n}$$ admits a section.

Some algebraic and topological properties of the nonabelian tensor product

Several authors investigated the properties which are invariant under the passage from a group to its nonabelian tensor square. In the present note we study this problem from the viewpoint of the classes of groups and the methods allow us to prove a result of invariance for some geometric properties of discrete groups.

Smooth 4-Dimensional Thickening of Singular 2-Dimensional Complex in the non Compact Case.

L'articolo estende la teoria dell'ingrossamento 4-dimensionale nel caso non-proprio.

On the 1-handles of the product V3XBn for a simply connected open 3-manifold V3

Although \pi_1^\inftyV^3 is an obstruction for killing stably the 1-handles of an open simply connected 3-manifold V^3, one can always get rid of the 1-handles of V^3\times B^n, for high enough n, at price of a certain nonmetrizable slackening of the topology.

A Group-Theoretical Finiteness Theorem