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Fiberations of free-by-cyclic groups

Connections for Women: Geometric Group Theory August 17, 2016 - August 19, 2016

August 19, 2016 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Yael Algom-Kfir (University of Haifa)
Location: MSRI: Simons Auditorium
  • automorphism groups

  • Out(F_n)

  • free-by-cyclic groups

  • Free Groups

  • Mapping Class Group

  • geometric group theory

  • folded mapping torus

  • semidirect products

  • fibrations

  • dilations

  • train-track maps

  • Dowdall-Kapovich-Leininger's construction

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



There is a beautiful and well developed theory (due to Thurston, Fried and McMullen) classifying all of the fiberations over the circle of a given 3-manifold.

These fibrations have common characteristics in particular if one fibration has a monodromy that is pseudo-Anosov then all fibrations have this property, and the dilatations are related via an element in the group ring of the first homology of the manifold.

We will discuss a theory of fiberations of free-by-cyclic groups that was developed in analogy to the 3-manifold case. 

In particular we will discuss Dowdall-Kapovich-Leininger's construction of an open cone of fiberations of a free-by-cyclic group, and their theorem that if the original outer automorphism was fully irreducible then the monodromy of each element in this cone is an irreducible train-track map. 

We then describe a polynomial that packages all of the dilatations of all of these train-track maps (by joint work with Hironaka and Rafi). 

26551?type=thumb Algom-Kir 803 KB application/pdf Download
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