Data

NameVilches Alarcón, José Antonio
DepartmentGeometría y Topología
Knowledge areaGeometría y Topología
Professional categoryProfesor Contratado Doctor
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  Statistics

  • Items

    17

  • Visits

    1620

  • Downloads

    3378

  Publications

 

Master's Final Project
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Funciones de Morse Excelentes en Pseudosuperficies trianguladas

Fernández Ternero, Desamparados; Vilches Alarcón, José Antonio; Luque Amaro, Álvaro (2022-06-15)
El objetivo principal de este trabajo es determinar cuántas funciones de Morse discretas excelentes (inyectivas para los ...
Final Degree Project
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Teoría de morse discreta

Vilches Alarcón, José Antonio; Ballesteros Hernández, Alejandro (2022-06-14)
Since it was introduced by Marston Morse in the 1920s, Morse Theory has been one of the most powerful and useful tool for ...
Article
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Morse–Bott theory on posets and a homological Lusternik–Schnirelmann theorem

Fernández Ternero, Desamparados; Macías Virgós, Enrique; Mosquera Lois, David; Vilches Alarcón, José Antonio (World Scientific Publishing Company, 2021-01-01)
We develop Morse–Bott theory on posets, generalizing both discrete Morse–Bott theory for regular complexes and Morse theory ...
Final Degree Project
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La topología gráfica sobre torneos

Fernández Ternero, Desamparados; Vilches Alarcón, José Antonio; Sánchez Ruíz, Ana Belén (2020-09-11)
El objetivo de esta memoria es definir una topología no trivial sobre torneos, no solo finitos, sino torneos infinitos ...
Article
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Structural aspects of the non-uniformly continuous functions and the unbounded functions within C(X)

Ayala Gómez, Rafael; Bernal González, Luis; Calderón Moreno, María del Carmen; Vilches Alarcón, José Antonio (Elsevier, 2019-04-01)
We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, ...
Article
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Simplicial Lusternik-Schnirelmann category

Fernández Ternero, Desamparados; Macías Virgós, Enrique; Minuz, Erica; Vilches Alarcón, José Antonio (Universidad Autónoma de Barcelona, 2019-01-01)
The simplicial LS-category of a nite abstract simplicial complex is a new invariant of the strong homotopy type, de ned ...
Final Degree Project
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Una Introducción a la pretopología

Ayala Gómez, Rafael; Vilches Alarcón, José Antonio; Velaure Valera, Elena (2019-01-01)
The main goal of this Final Degree Project is the study of pretopological spaces. Being more precise, certain properties ...
Final Degree Project
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Espacios pretopológicos: algunas aplicaciones

Ayala Gómez, Rafael; Vilches Alarcón, José Antonio; González Puntas, Gloria (2018-01-01)
The goal of this work is to study the theory of pretopological spaces and some applications. Starting with the key notion ...
Final Degree Project
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Sobre las diferentes nociones topológicas de complejo y algunas de sus aplicaciones

Ayala Gómez, Rafael; Vilches Alarcón, José Antonio; Núñez de Arco Valenzuela, Laura (2016-12-01)
The main goal of this work is to introduce the different kinds of combinatorial structures used in topological data analysis. ...
Final Degree Project
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La categoría de Lusternik-Schnirelmann de los espacios finitos. Enunciado y discusión de un problema

Quintero Toscano, Antonio Rafael; Vilches Alarcón, José Antonio; Pavón Díaz, Álvaro (2016-01-01)
El trabajo presenta el invariante homotópico conocido como categoría de Lusternik-Schnirelmann (categoría LS, para ...
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Lusternik-Schnirelmann category of simplicial complexes and finite spaces

Fernández Ternero, Desamparados; Macías Virgós, Enrique; Vilches Alarcón, José Antonio (Elsevier, 2015-10-01)
In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well ...
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Counting excellent discrete Morse functions on compact orientable surfaces

Ayala Gómez, Rafael; Fernández Ternero, Desamparados; Vilches Alarcón, José Antonio (Universidad de Sevilla, 2010-01-01)
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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Perfect discrete Morse functions on 2-complexes

Ayala Gómez, Rafael; Fernández Ternero, Desamparados; Vilches Alarcón, José Antonio (Universidad de Sevilla, 2010-01-01)
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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Discrete Morse inequalities on infinite graphs

Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio; Ayala Gómez, Rafael (2009-01-01)
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Critical elements of proper discrete Morse functions

Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio (Editorial Board of Mathematica Pannonica, 2008-01-01)
The aim of this paper is to study the notion of critical element of a proper discrete Morse function defined on non-compact ...
PhD Thesis
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Funciones de Morse discretas sobre complejos infinitos

Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio (2003-01-01)
Esta memoria está dedicada a la extensión para complejos simpliciales infinitos de los conceptos y resultados de la teoría ...
Presentation
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Desigualdades de Morse generalizadas sobre grafos

Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio (Alberto Márquez, 2002-01-01)