Fiberations of freebycyclic groups
Connections for Women: Geometric Group Theory August 17, 2016  August 19, 2016
Location: SLMath: Eisenbud Auditorium
automorphism groups
Out(F_n)
freebycyclic groups
Free Groups
Mapping Class Group
geometric group theory
folded mapping torus
semidirect products
fibrations
dilations
traintrack maps
DowdallKapovichLeininger's construction
20Jxx  Connections of group theory with homological algebra and category theory
00A35  Methodology of mathematics {For mathematics education, see 97XX}
14585
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 3manifold.
These fibrations have common characteristics in particular if one fibration has a monodromy that is pseudoAnosov 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 freebycyclic groups that was developed in analogy to the 3manifold case.
In particular we will discuss DowdallKapovichLeininger's construction of an open cone of fiberations of a freebycyclic 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 traintrack map.
We then describe a polynomial that packages all of the dilatations of all of these traintrack maps (by joint work with Hironaka and Rafi).
AlgomKir

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