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Arturo Espinosa Baro

Publications and source records attributed to Arturo Espinosa Baro.

6 recordsLinked to original sources
arXiv2026

On open covers of aspherical spaces satisfying $π_1$-constraints and bounded Adamson cohomology

Given a topological space $X$ and a family of subgroups $\mathcal{F}$ of $π_1(X)$, the $\mathcal{F}$-category of $X$ is given as one less than the cardinality of the smallest cover of $X$ by open subsets whose fundamental groups lie in $\mathcal{F}$. In this article we study $\mathcal{F}$-categories of aspherical spaces and obtain cohomological lower bounds, a maximality result and bounded cohomology classes whose vanishing properties are crucial for determining $\mathcal{F}$-categories. For this purpose, we study the bounded Adamson cohomology of a family of subgroups and discuss universality properties of bounded cohomology classes. We apply our techniques to derive some applications to the study of the monotonicity of $\mathcal{F}$-categories under degree-one maps between manifolds and to provide a counterexample to a question of Capovilla, Löh and Moraschini.

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arXiv2025

Sectional category of subgroup inclusions and sequential topological complexities of aspherical spaces as A-genus

In this paper we characterize the sectional category of subgroup inclusions and the $r^{th}$-sequential topological complexity of aspherical spaces of a group G in terms of the A-genus in the sense of Clapp-Puppe and Bartsch for a suitable one-element family of G-spaces A, and we discuss some of the consequences of such characterization, including new ideas about notions of category-like invariants with respect to proper actions of groups.

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arXiv2024

On properties of effective topological complexity and effective Lusternik-Schnirelmann category

The notion of effective topological complexity, introduced by Błaszczyk and Kaluba, deals with using group actions in the configuration space in order to reduce the complexity of the motion planning algorithm. In this article we focus on studying several properties of such notion of topological complexity. We introduce a notion of effective LS-category which mimics the behaviour the usual LS-cat has in the non-effective setting. We use it to investigate the relationship between these effective invariants and the orbit map with respect of the group action, and we give numerous examples. Additionally, we investigate non-vanishing criteria based on a cohomological dimension bound of the saturated diagonal.

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arXiv2023

On the sectional category of subgroup inclusions and Adamson cohomology theory

The sectional category of a subgroup inclusion $H \hookrightarrow G$ can be defined as the sectional category of the corresponding map between Eilenberg--MacLane spaces. We extend a characterization of topological complexity of aspherical spaces given by Farber, Grant, Lupton and Oprea to the context of sectional category of subgroup inclusions and investigate it by means of Adamson cohomology theory.

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arXiv2023

Sequential topological complexity of aspherical spaces and sectional categories of subgroup inclusions

We generalize results from topological robotics on the topological complexity (TC) of aspherical spaces to sectional categories of fibrations inducing subgroup inclusions on the level of fundamental groups. In doing so, we establish new lower bounds on sequential TCs of aspherical spaces as well as the parametrized TC of epimorphisms. Moreover, we generalize the Costa-Farber canonical class for TC to classes for sequential TCs and explore their properties. We combine them with the results on sequential TCs of aspherical spaces to obtain results on spaces that are not necessarily aspherical.

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