000087133 001__ 87133 000087133 005__ 20210520140811.0 000087133 037__ $$aTESIS-2020-020 000087133 041__ $$aeng 000087133 080__ $$a51 000087133 1001_ $$aBlasco García, Rubén 000087133 24500 $$aEven Artin Groups 000087133 260__ $$aZaragoza$$bUniversidad de Zaragoza, Prensas de la Universidad$$c2019 000087133 300__ $$a145 000087133 4900_ $$aTesis de la Universidad de Zaragoza$$v2020-20$$x2254-7606 000087133 500__ $$aPresentado: 03 09 2019 000087133 502__ $$aTesis-Univ. Zaragoza, Matemáticas, 2019$$bZaragoza, Universidad de Zaragoza$$c2019 000087133 506__ $$aall-rights-reserved 000087133 520__ $$aRight-angled Artin groups form an interesting family of groups both from an<br />algebraic and a topological point of view. There are a lot of well-known properties<br />of right-angled Artin groups: for example they are poly-free, locally<br />indicable, right orderable and residually finite. Besides, also many important<br />problems are well understood for these groups such as the word problem, the<br />rigidity problem, Serre's question or the K(pi, 1) conjecture.<br />In this thesis, we will study some of these properties for a bigger and<br />interesting subfamily of Artin groups: even Artin groups. We generalize<br />many of these properties either for even Artin groups in full genarility or for<br />some big and interesting subfamilies.<br />In particular, we prove that even Artin groups of FC type and large even<br />Artin groups are poly-free (which, as we will see, implies that they are also<br />locally indicable and right orderable) and that even Artin groups of FC type<br />and general Artin groups based on trees are residually finite. Finally, we<br />answer Serre's question for the whole family of even Artin groups.<br /> 000087133 520__ $$a<br /> 000087133 521__ $$97078$$aPrograma de Doctorado en Matemáticas y Estadística 000087133 6531_ $$agrupos generalidades 000087133 6531_ $$ageometria algebraica 000087133 700__ $$aMartínez Pérez, Concepción$$edir. 000087133 700__ $$aCogolludo Agustín, José Ignacio$$edir. 000087133 7102_ $$aUniversidad de Zaragoza$$bMatemáticas 000087133 830__ $$9490 000087133 8560_ $$ftdr@unizar.es 000087133 8564_ $$s1455475$$uhttps://zaguan.unizar.es/record/87133/files/TESIS-2020-020.pdf$$zTexto completo (eng) 000087133 909CO $$ooai:zaguan.unizar.es:87133$$pdriver 000087133 909co $$ptesis 000087133 9102_ $$a$$bMatemáticas 000087133 980__ $$aTESIS