FERNÁNDEZ LASHERAS , Francisco Jesús

We are concerned with the implications of the Freiheitssatz property for certain group presentations in terms of proper homotopy invariants of the underlying group, by describing its fundamental pro-group. A finitely presented group G is said to be properly 3-realizable if it is the fundamental group of a finite 2-dimensional CW-complex whose...

If a finitely generated group G maps epimorphically onto a group H, we are interested in the question: When does the semistability of H imply G is semistable? In this paper, we give an answer within the class of ascending HNNextensions. More precisely, our main theorem states: Suppose that the 1-ended finitely generated ascending HNN-extension...

A group is properly 3-realizable if it is the fundamental group of a compact polyhedron whose universal covering is proper homotopically equivalent to some 3-manifold. We prove that when such a group is also quasi-simply filtered then it has pro-(finitely generated free) fundamental group at infinity and semi-stable ends. Conjecturally the...

Direccion General de Investigacion Cientifica y Tecnica

Classical results about the Lusternik-Schnirelmann category of product spaces have their analogues in the category of proper maps. By comparing the proper Lusternik-Schnirelmann category of an open manifold X with the smallest number of closed half-spaces needed to cover X, we obtain a proper analogue of Singhof's theorem on the category of X × S1.

Motivated by the notion of boundary for hyperbolic and groups, Bestvina [2] introduced the notion of a (weak) -structure and (weak) -boundary for a group G of type (i.e., having a finite complex), with implications concerning the Novikov conjecture for G. Since then, some classes of groups have been shown to admit a weak -structure...

We recall that a finitely presented group G is properly 3-realizable if for some finite 2-dimensional CW-complex X with π1(X) ∼= G, the universal cover X has the proper homotopy type of a 3-manifold. This purely topological property is closely related to the asymptotic behavior of the group G. We show that proper 3-realizability is also a...

In this paper, we show that the class of all properly 3-realizable groups is closed under amalgamated free products (and HNN-extensions) over finite groups. We recall that G is said to be properly 3-realizable if there exists a compact 2-polyhedron K with π1(K)≅G and whose universal cover View the MathML source has the proper homotopy type of a...

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces.

How different is the universal cover of a given finite 2-complex from a 3-manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group G is said to be properly 3-realizable if there exists a compact 2-polyhedron K with π1(K) ∼= G whose universal cover K˜ has the proper homotopy type of a PL...

Recall that two finitely presented groups G and H are "proper 2–equivalent" if they can be realized by finite 2–dimensional CW–complexes whose universal covers are proper 2–equivalent as (strongly) locally finite CW–complexes. This purely topological relation is coarser than the quasi-isometry relation, and those groups which are 1–ended and...

In this paper, we consider an equivalence relation within the class of finitely presented discrete groups attending to their asymptotic topology rather than their asymptotic geometry. More precisely, we say that two finitely presented groups G and H are "proper 2-equivalent" if there exist (equivalently, for all) finite 2-dimensional...