English
Endomorphisms, train track maps, and fully irreducible monodromies
Post-edited
Auteurs : Kapovich, Ilya (Auteur de la Conférence)
CIRM (Editeur )
20F65 - Geometric group theory
37Bxx - topological dynamics
37Dxx - Dynamical systems with hyperbolic behavior
57Mxx - Low-dimensional topology
CIRM (Editeur )
Résumé :
An endomorphism of a finitely generated free group naturally descends to an injective endomorphism on the stable quotient. We establish a geometric incarnation of this fact : an expanding irreducible train track map inducing an endomorphism of the fundamental group determines an expanding irreducible train track representative of the injective endomorphism of the stable quotient. As an application, we prove that the property of having fully irreducible monodromy for a splitting of a hyperbolic free-by-cyclic group G depends only on the component of the BNS invariant $\sum \left ( G \right )$ containing the associated homomorphism to the integers. In particular, it follows that if G is the mapping torus of an atoroidal fully irreducible automorphism of a free group and if the union of $\sum \left ( G \right ) $ and $\sum \left ( G \right )$ is connected then for every splitting of $G$ as a (f.g. free)-by-(infinite cyclic) group the monodromy is fully irreducible.
This talk is based on joint work with Spencer Dowdall and Christopher Leininger.
Codes MSC : This talk is based on joint work with Spencer Dowdall and Christopher Leininger.
20F65 - Geometric group theory
37Bxx - topological dynamics
37Dxx - Dynamical systems with hyperbolic behavior
57Mxx - Low-dimensional topology
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 30/07/15 Date de captation : 13/07/15 Sous collection : Research talks arXiv category : Group Theory ; Dynamical Systems ; Geometric Topology Domaine : Algebra ; Dynamical Systems & ODE ; Topology ; Geometry Format : QuickTime (.mov) Durée : 1:06:18 Audience : Researchers Download : https://videos.cirm-math.fr/2015-07-13_Kapovich.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Impact of geometric group theory / Impacts de la géométrie des groupesOrganisateurs de la rencontre : Arzhantseva, Goulnara N. ; Bedaride, Nicolas ; Gaboriau, Damien ; Hilion, Arnaud Dates : 13/07/15 - 17/07/15 Année de la rencontre : 2015 URL Congrès : http://conferences.cirm-math.fr/1224.html
Données de citation
DOI : 10.24350/CIRM.V.18799003Citer cette vidéo: Kapovich, Ilya (2015). Endomorphisms, train track maps, and fully irreducible monodromies. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18799003 URI : http://dx.doi.org/10.24350/CIRM.V.18799003 |
Voir aussi
- [Multi angle] Natural subgroups of automorphisms / Auteur de la Conférence Guirardel, Vincent.
- [Multi angle] Full groups, cost, symmetric groups and IRSS / Auteur de la Conférence Le Maître, François.
- [Multi angle] Growth under random products of automorphisms of a free group / Auteur de la Conférence Horbez, Camille.
- [Multi angle] Kazhdan projections / Auteur de la Conférence Drutu, Cornelia.
Bibliographie
- Dowdall, S., Kapovich, I., & Leininger, Christopher J. (2015). Endomorphisms, train track maps, and fully irreducible monodromies.
