Endomorphisms, train track maps, and fully irreducible monodromies | Vidéo | Carmin.tv

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Endomorphisms, train track maps, and fully irreducible monodromies

By Ilya Kapovich

Appears in collection : Impact of geometric group theory / Impacts de la géométrie des groupes

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.

Information about the video

Date of recording 13/07/2015
Date of publication 30/07/2015
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18799003
Cite this video Kapovich, Ilya (13/07/2015). Endomorphisms, train track maps, and fully irreducible monodromies. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18799003
URL https://dx.doi.org/10.24350/CIRM.V.18799003

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Bibliography

Dowdall, S., Kapovich, I., & Leininger, Christopher J. (2015). Endomorphisms, train track maps, and fully irreducible monodromies. <arXiv:1507.03028> - http://xxx.tau.ac.il/abs/1507.03028

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