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Artículo
Homotopy in digital spaces
(Elsevier, 2003-01-15)
The main contribution of this paper is a new “extrinsic” digital fundamental group that can be readily generalized to define higher homotopy groups for arbitrary digital spaces. We show that the digital fundamental group ...
Artículo
Approximation axiomatique à la théorie du bordisme
(Université de Picardie Jules Verne, 1989)
This paper gives an axiomatical approximation to Bordism Theory. It proves those properties of a geometrical nature that a class of models must satisfy to develop a bordism theory in an abstract category.
Artículo
The equivariant category of proper G-Spaces
(Rocky Mountain Mathematics Consortium, 2001)
Artículo
A digital index theorem
(World Scientific Publishing, 2001-11)
This paper is devoted to prove a Digital Index Theorem for digital (n − 1)-manifolds in a digital space (Rn, f), where f belongs to a large family of lighting functions on the standard cubical decomposition Rn of the ...
Artículo
Digital homotopy with obstacles
(Elsevier, 2004-04-30)
As a sequel of [4] Ayala, R., E. Dom´ıguez, A. R. Franc´es and A. Quintero, Homotopy in Digital Spaces, Discrete and Applied Mathematics, To Appear, this paper is devoted to the computation of the digital fundamental group ...
Artículo
Exponential law for uniformly continous proper maps
(Universitat Autònoma de Barcelona, 1988)
The purpose of this note is to prove the exponential law for uniformly continuous proper maps.
Artículo
Lusternik-Schnirelmann invariants in proper homotopy theory
(University of California, 1992)
We introduce and study proper homotopy invariants of the Lusternik-Schnirelmann type, p-cat (-), p-Cat(-), and cat e(-) in the category of Γ2-locally compact spaces and proper maps. As an application, Rn (n Φ 3) is ...
Artículo
On the connectivity of skeletons of pseudomanifolds with boundary
(Mathematical Institute, Academy of Sciences of the Czech Republic, 2002)
In this note we show that 1-skeletons and 2-skeletons of n-pseudomanifolds with full boundary are (n+ 1)-connected graphs and n-connected 2-complexes, respectively. This generalizes previous results due to Barnette and Woon.
Ponencia
On surfaces in digital topology
(1995)
In R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, J. Rubio. A Polyhedral Approach to Digital Topology a new framework for digital topology has been proposed. This framework offers the possibility of transfering, in an ...
Artículo
A note on the homotopical characterization of Rn
(Universitat de Barcelona, 1992)
This note gives conditions which assure that the one-point compactification of an open manifold is a manifold. This result is used to show that the homotopical characterization of Rn (n ≥ 4) can be derived from the Poincaré ...