000152369 001__ 152369
000152369 005__ 20250401114421.0
000152369 037__ $$aTAZ-TFM-2024-1276
000152369 041__ $$aeng
000152369 1001_ $$aAlquézar Baeta, Carlos
000152369 24200 $$aEffective computation of the Sullivan model of a topological space and its rational homotopy type.
000152369 24500 $$aCálculo efectivo del modelo de Sullivan de un espacio topológico y su tipo de homotopía racional.
000152369 260__ $$aZaragoza$$bUniversidad de Zaragoza$$c2024
000152369 506__ $$aby-nc-sa$$bCreative Commons$$c3.0$$uhttp://creativecommons.org/licenses/by-nc-sa/3.0/
000152369 520__ $$aThe rational homotopy type of a topological space is a simplified version of the homotopy type where all homotopy groups are tensored by Q. Despite the lost information, rational homotopy has the advantage of being constructive. Due to Sullivan, for a particular topological space X that satisfies some conditions, it is known theoretically how to obtain its rational homotopy type via the construction of a commutative differential graded algebra, called the Sullivan model of X. This algebra is quasi-isomorphic to the normalized singular cochain algebra of X, C*(X), and it allows us to establish a categorical equivalence between homotopy types of spaces and isomorphism classes of Sullivan models. In this work it is presented an effective method to compute the Sullivan minimal model for a simply-connected topological space, and an implementation of such method in a Computer Algebra System. In order to illustrate such method, examples of some computations are included.<br /><br />
000152369 521__ $$aMáster Universitario en Modelización e Investigación Matemática, Estadística y Computación
000152369 540__ $$aDerechos regulados por licencia Creative Commons
000152369 691__ $$a0
000152369 692__ $$a
000152369 700__ $$aMarco Buzunáriz, Miguel Ángel$$edir.
000152369 700__ $$aMartín Morales, Jorge$$edir.
000152369 7102_ $$aUniversidad de Zaragoza$$bMatemáticas$$cGeometría y Topología
000152369 8560_ $$falquezar@unizar.es
000152369 8564_ $$s536264$$uhttps://zaguan.unizar.es/record/152369/files/TAZ-TFM-2024-1276.pdf$$yMemoria (eng)
000152369 909CO $$ooai:zaguan.unizar.es:152369$$pdriver$$ptrabajos-fin-master
000152369 950__ $$a
000152369 951__ $$adeposita:2025-04-01
000152369 980__ $$aTAZ$$bTFM$$cCIEN
000152369 999__ $$a20240910122918.CREATION_DATE