Espacios recubridores: un enfoque gráfico de la teoría

Abstract

This work addresses fundamental concepts of algebraic topology, focusing on group actions on topological spaces. It explores structures such as quotient spaces, orbits, and covering spaces, using examples like the action of the integer group on the real line and the antipodal action on the sphere, leading to the construction of spaces such as the circle, the torus, and the projective plane. Additionally, it examines the relationship between properly discontinuous groups and covering spaces, as well as the importance of covering transformations and the fundamental group in understanding the algebraic structure of spaces.