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H 2 Endomorphisms, train track maps, and fully irreducible monodromies

Auteurs : Kapovich, Ilya (Auteur de la Conférence)
CIRM (Editeur )

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BNS invariant free-by-cyclic group free group monodromy fully irreducible automorphism train track map folded mapping torus semi-flow fully irreducible criterion free groups endomorphisms stable quotient

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 :
20F65 - Geometric group theory
37BXX - topological dynamics
37Dxx - Dynamical systems with hyperbolic behavior
57Mxx - Low-dimensional topology

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 30/07/15
    Date de captation : 13/07/15
    Collection : Research Talks ; Algebra ; Dynamical Systems and Ordinary Differential Equations ; Geometry ; Topology
    Format : QuickTime (.mov) Durée : 1:06:18
    Domaine : Algebra ; Dynamical Systems & ODE ; Topology ; Geometry
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2015-07-13_Kapovich.mp4

Informations sur la rencontre

Nom de la rencontre : Impact of geometric group theory / Impacts de la géométrie des groupes
Organisateurs 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

Citation Data

DOI : 10.24350/CIRM.V.18799003
Cite this video as: 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

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