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A∞-persistence
Belchi-Guillamón, Francisco (Servicio de Publicaciones y Divulgación Científica, 2015)This work is a mixture of two different worlds: Persistent Homology and A∞-(co)algebras. The former is a new tool in Topological Data Analysis, whilst the latter is a classical concept in Homological Perturbation ... -
Infinity structures and higher products in rational homotopy theory
Moreno-Fernández, José Manuel (UMA Editorial, 2018)Rational homotopy theory classically studies the torsion free phenomena in the homotopy category of topological spaces and continuous maps. Its success is mainly due to the existence of relatively simple algebraic models ... -
Lie models of classifying fibrations.
Fuentes Rumí, Mario (UMA Editorial, 2023)En el ámbito de la Teoría de Homotopía Racional, los recientemente desarrollados modelos de Lie, permiten la modelización de espacios topológicos no simplemente conexos. En esta tesis se utiliza esta nueva técnica para ... -
Lie models of homotopy automorphism monoids and classifying fibrations
Félix, Yves; Fuentes Rumí, Mario; Murillo-Mas, Aniceto (Elsevier, 2022-06-25)Given X a finite nilpotent simplicial set, consider the classifying fibrations X → B aut∗ G(X) → B autG(X) and X → Z → B aut∗ π (X) where G and π denote, respectively, subgroups of the free and pointed homotopy classes ... -
The Achievement Set of Generalized Multigeometric Sequences
Karvatskyi, Dmytro; Murillo-Mas, Aniceto; Viruel-Arbaizar, Antonio Ángel (Springer, 2024-04-13)We study the topology of all possible subsums of the generalized multigeometric series where are fixed positive real numbers and f runs along a certain class of non-negative functions on the unit interval. We detect ...