Now showing items 1-9 of 9

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      A note on the homotopical characterization of Rn  [Article]

      Ayala Gómez, Rafael; Quintero Toscano, Antonio Rafael (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 ...
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      Approximation axiomatique à la théorie du bordisme  [Article]

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Quintero Toscano, Antonio Rafael (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.
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      Critical elements of proper discrete Morse functions  [Article]

      Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio (Editorial Board of Mathematica Pannonica, 2008)
      The aim of this paper is to study the notion of critical element of a proper discrete Morse function defined on non-compact graphs and surfaces. It is an extension to the non-compact case of the concept of critical simplex ...
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      Discrete Morse inequalities on infinite graphs  [Article]

      Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio; Ayala Gómez, Rafael (2009)
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      Homotopy in digital spaces  [Article]

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Francés Román, Ángel Ramón; Quintero Toscano, Antonio Rafael (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 ...
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      Lusternik-Schnirelmann invariants in proper homotopy theory  [Article]

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Márquez Pérez, Alberto; Quintero Toscano, Antonio Rafael (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 ...
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      On surfaces in digital topology  [Presentation]

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Francés Román, Ángel Ramón; Quintero Toscano, Antonio Rafael; Rubio Sender, Julio (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 ...
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      On the connectivity of skeletons of pseudomanifolds with boundary  [Article]

      Ayala Gómez, Rafael; Chávez de Diego, María José; Márquez Pérez, Alberto; Quintero Toscano, Antonio Rafael (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.
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      The equivariant category of proper G-Spaces  [Article]

      Ayala Gómez, Rafael; Fernández Lasheras, Francisco Jesús; Quintero Toscano, Antonio Rafael (Rocky Mountain Mathematics Consortium, 2001)