Modellng of the fundamental group of a knot as a strategy for establishing a surface structure

Abstract

Background

teaching practice shows little development of mathematical competences in students to provide a satisfactory response to everyday situations, manifested in difficulties in identifying topology as a tool that allows modeling this type of situation.

Objective

to develop and implement a mathematical modeling proposal involving topology as a way of connecting the real world with mathematics.

Methodology

action research with a qualitative approach was carried out with fifty university students. Analysis and results: the importance of studying topological invariants is highlighted because they allow us to find differences and similarities in closed three-dimensional trajectories, elements that make up the structure of a surface. The importance of: relating metric spaces with topology; the need to handle and institutionalise a clear, precise, and proper language of topology as components that allow the student to recognise that the topological properties of knots (invariants) are directly related to the properties of the surfaces that can be generated from them.

Topology; Topological invariant; Knot theory; Fundamental group