Alejandro O. Majadas-Moure

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20232026

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math.AT2026

Singular multivalued homology

Alejandro O. Majadas-Moure

Let $X$ be a compact, Hausdorff topological space. Then $H_{n}^{M} (X) = 0$ for all $n > 0$ , where $H_{n}$ is the multivalued analogue of singular homology. The case $n = 1$ is already known [8…

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.AT2026

New Applications and Computations of the Lefschetz Number of Homeomorphisms and Open Maps

Jesús A. Álvarez López, Alejandro O. Majadas-Moure

We show that the combinatorial Lefschetz number is a topological invariant. This is an important result in itself; in order to point it out, we will also work here several relevant…

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…