David Mosquera-Lois

activity

20232026

collaborators

6 papers

math.AT2026

Weak, stable, and ordinary Lusternik-Schnirelmann category of finite spaces

David Mosquera-Lois, Kohei Tanaka

The weak, stable, and ordinary Lusternik--Schnirelmann categories of a finite $T_{0}$ -space $X$ satisfy $\operatorname{cat}_w(X)\leq \operatorname{cat}_s(X)\leq \operatorname{cat}(X)…

math.AT2026

Whitehead's theorem for minimal finite models

David Mosquera-Lois

We investigate the extent to which Whitehead's theorem remains valid for minimal finite models. We show that it fails in this setting, answering negatively a question posed by Barm…

math.AT2026

Morse-Bott inequalities for endomorphisms

Enrique Macías-Virgós, Alejandro O. Majadas-Moure, David Mosquera-Lois +1

Let $K$ be a finite simplicial complex, let $g : K \to K$ be a simplicial map and let $f$ be a discrete Morse-Bott function on $K$ satisfying $f (g (σ)) \leq f (σ)$ for all simplice…

math.AT2025

A Combinatorial Study of the Fixed Point Index

Jesús A. Álvarez López, Alejandro O. Majadas-Moure, David Mosquera-Lois

We introduce a theory of integration with respect to the fixed point index, offering a substantial improvement over previous approaches based on the Lefschetz number. This framewor…

math.AT2024

Sheaf Theoretic Approach to Lefschetz Calculus

Alejandro O. Majadas-Moure, David Mosquera-Lois

We lift the Lefschetz number from an algebraic invariant of maps between spaces to an invariant of morphisms of data over the spaces.

math.AT2023

Integration with respect to the Lefschetz number

Alejandro O. Majadas-Moure, David Mosquera-Lois

We develop a theory of integration with respect to the Lefschetz number in the context of o-minimal structures containing the semilinear sets. We prove several results and we apply…