Now showing items 1-20 of 22

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      A digital index theorem  [Article]

      Domínguez Murillo, Eladio; Francés Román, Ángel Ramón; Ayala Gómez, Rafael; Quintero Toscano, Antonio Rafael (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 ...
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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 Conjecture.
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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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      Aproximación axiomática a las teorías de cobordismo  [PhD Thesis]

      Ayala Gómez, Rafael (1982)
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      Counting excellent discrete Morse functions on compact orientable surfaces  [Article]

      Ayala Gómez, Rafael; Fernández Ternero, Desamparados; Vilches Alarcón, José Antonio (Universidad de Sevilla, 2010)
      We obtain the number of non-homologically equivalent excellent discrete Morse functions defined on compact orientable surfaces. This work is a continuation of the study which has been done in [2, 4] for graphs.
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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 ...
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      Defining discrete Morse functions on infinite surfaces  [Presentation]

      Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel (2004)
      We present an algorithm which defines a discrete Morse function in Forman’s sense on an infinite surface including a study of the minimality of this function.
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      Desigualdades de Morse generalizadas sobre grafos  [Presentation]

      Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio (Alberto Márquez, 2002)
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      Digital homotopy with obstacles  [Article]

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Francés Román, Ángel Ramón; Quintero Toscano, Antonio Rafael (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 ...
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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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      Espacios pretopológicos: algunas aplicaciones  [Final Degree Work]

      González Puntas, Gloria (2018)
      The goal of this work is to study the theory of pretopological spaces and some applications. Starting with the key notion ...
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      Exponential law for uniformly continous proper maps  [Article]

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Quintero Toscano, Antonio Rafael (Universitat Autònoma de Barcelona, 1988)
      The purpose of this note is to prove the exponential law for uniformly continuous proper maps.
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      Funciones de Morse discretas sobre complejos infinitos  [PhD Thesis]

      Vilches Alarcón, José Antonio (2003)
      Esta memoria está dedicada a la extensión para complejos simpliciales infinitos de los conceptos y resultados de la teoría ...
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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 ...
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      Una Introducción a la pretopología  [Final Degree Work]

      Velaure Valera, Elena (2019)
      The main goal of this Final Degree Project is the study of pretopological spaces. Being more precise, certain properties ...
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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(-) ...
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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 ...
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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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      Perfect discrete Morse functions on 2-complexes  [Article]

      Ayala Gómez, Rafael; Fernández Ternero, Desamparados; Vilches Alarcón, José Antonio (Universidad de Sevilla, 2010)
      This paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete ...
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      Sobre las diferentes nociones topológicas de complejo y algunas de sus aplicaciones  [Final Degree Work]

      Núñez de Arco Valenzuela, Laura (2016-12)
      The main goal of this work is to introduce the different kinds of combinatorial structures used in topological data ...