Even artin groups

• Autores: Ruben Blasco Garcia
• Directores de la Tesis: Concepción Martínez Pérez (dir. tes.) , José Ignacio Cogolludo Agustín (dir. tes.)
• Lectura: En la Universidad de Zaragoza ( España ) en 2019
• Idioma: español
• Tribunal Calificador de la Tesis: Javier Otal Cinca (presid.) , Yago Antolín Pichel (secret.) , Botong Wang (voc.)
• Enlaces
  • Tesis en acceso abierto en: Zaguán
• Resumen

  • Right-angled Artin groups form an interesting family of groups both from an algebraic and a topological point of view. There are a lot of well-known properties of right-angled Artin groups: for example they are poly-free, locally indicable, right orderable and residually finite. Besides, also many important problems are well understood for these groups such as the word problem, the rigidity problem, Serre's question or the K(pi, 1) conjecture.

    In this thesis, we will study some of these properties for a bigger and interesting subfamily of Artin groups: even Artin groups. We generalize many of these properties either for even Artin groups in full genarility or for some big and interesting subfamilies.

    In particular, we prove that even Artin groups of FC type and large even Artin groups are poly-free (which, as we will see, implies that they are also locally indicable and right orderable) and that even Artin groups of FC type and general Artin groups based on trees are residually finite. Finally, we answer Serre's question for the whole family of even Artin groups.