CÁRDENAS ESCUDERO , Manuel Enrique

En la tesis que se presenta se extienden fundamentalmente algunos resultados y metodologías de mediados de los años 80 y 90 sobre la k-categoría algebraica de categorías aditivas al estudio de la k-categoría algebraica de las categoría ... En el tercer capítulo se mejoran algunos resultados ya conocidos de categorías exactas, que se han...

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...

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...