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Endomorphisms, train track maps, and fully irreducible monodromies
Post-edited
Authors : Kapovich, Ilya (Author of the conference)
CIRM (Publisher )
20F65 - Geometric group theory
37Bxx - topological dynamics
37Dxx - Dynamical systems with hyperbolic behavior
57Mxx - Low-dimensional topology
CIRM (Publisher )
Abstract :
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.
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 30/07/15 Conference Date : 13/07/15 Subseries : Research talks arXiv category : Group Theory ; Dynamical Systems ; Geometric Topology Mathematical Area(s) : Algebra ; Dynamical Systems & ODE ; Topology ; Geometry Format : QuickTime (.mov) Video Time : 1:06:18 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-07-13_Kapovich.mp4 
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Information on the Event
Event Title : Impact of geometric group theory / Impacts de la géométrie des groupesEvent Organizers : Arzhantseva, Goulnara N. ; Bedaride, Nicolas ; Gaboriau, Damien ; Hilion, Arnaud Dates : 13/07/15 - 17/07/15 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1224.html
Citation Data
DOI : 10.24350/CIRM.V.18799003Cite 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 |
See Also
- [Multi angle] Natural subgroups of automorphisms / Author of the conference Guirardel, Vincent.
- [Multi angle] Full groups, cost, symmetric groups and IRSS / Author of the conference Le Maître, François.
- [Multi angle] Growth under random products of automorphisms of a free group / Author of the conference Horbez, Camille.
- [Multi angle] Kazhdan projections / Author of the conference Drutu, Cornelia.
Bibliography
- Dowdall, S., Kapovich, I., & Leininger, Christopher J. (2015). Endomorphisms, train track maps, and fully irreducible monodromies.
