Teor\'ia de homotop\'ia usando conjuntos simpliciales

TL;DR

This paper provides an accessible introduction to homotopy theory using simplicial sets, emphasizing intuition and key results for students with basic topology knowledge.

Contribution

It offers a beginner-friendly guide to homotopy theory and simplicial methods, bridging foundational concepts with intuitive explanations.

Findings

Introduces simplicial sets as a tool for homotopy theory

Highlights key theorems and concepts in an accessible manner

Serves as an educational resource for students new to the field

Abstract

These lecture notes (in Spanish) are based on a mini-course given by A. Osorno and M. Rivera at the First Colombian Geometry and Topology Meeting that took place at the Universidad Nacional de Colombia in July 2024 in Bogota. They are intended to be a guide for a first encounter with homotopy theory and simplicial methods - emphasizing intuition and important statements - accessible to students with basic knowledge of point set topology. Estas notas surgieron como parte de un mini-curso dictado por A. Osorno y M. Rivera en el primer Encuentro Colombiano de Geometr\'ia y Topolog\'ia (ECOGyT) que se llev\'o a cabo en la Universidad Nacional de Colombia sede Bogot\'a en julio del 2024. La idea es que sirvan como una gu\'ia para un primer encuentro con la teor\'ia de homotop\'ia y t\'ecnicas simpliciales - enfatizando en la intuici\'on y enunciados importantes - accesible a estudiantes con conocimiento b\'asico de topolog\'ia general y as\'i invitar a indagar m\'as profundamente sobre el tema y sus aplicaciones en distintos campos.