Cálculo efectivo del modelo de Sullivan de un espacio topológico y su tipo de homotopía racional.

Alquézar Baeta, Carlos
Marco Buzunáriz, Miguel Ángel (dir.) ; Martín Morales, Jorge (dir.)

Universidad de Zaragoza, CIEN, 2024
Departamento de Matemáticas, Área de Geometría y Topología

Máster Universitario en Modelización e Investigación Matemática, Estadística y Computación

Resumen: The rational homotopy type of a topological space is a simplified version of the homotopy type where all homotopy groups are tensored by Q. Despite the lost information, rational homotopy has the advantage of being constructive. Due to Sullivan, for a particular topological space X that satisfies some conditions, it is known theoretically how to obtain its rational homotopy type via the construction of a commutative differential graded algebra, called the Sullivan model of X. This algebra is quasi-isomorphic to the normalized singular cochain algebra of X, C*(X), and it allows us to establish a categorical equivalence between homotopy types of spaces and isomorphism classes of Sullivan models. In this work it is presented an effective method to compute the Sullivan minimal model for a simply-connected topological space, and an implementation of such method in a Computer Algebra System. In order to illustrate such method, examples of some computations are included.

Tipo de Trabajo Académico: Trabajo Fin de Master