Dynamics of Irreducible Endomorphisms of the Free Group

Seminar: 
Geometry & Topology
Event time: 
Tuesday, November 9, 2010 - 11:30am to Monday, November 8, 2010 - 7:00pm
Location: 
431 DL
Speaker: 
Patrick Reynolds
Speaker affiliation: 
UIUC
Event description: 

We extend recent dynamical techniques for studying automorphisms
of the free group to injective endomorphisms. Focusing on the class of
endomorphisms that satisfy the Bestvina-Handel irreducibility criterion,
we characterize the dynamics on conjugacy classes and on the boundary of
the free group via a “train track” theorem. After imposing a (necessary)
additional hypothesis, we consider the action of an irreducible
endomorphism on the closure of the Culler-Vogtmann Outer space and show
that this action has “north dynamics”–there is a unique (attracting)
fixed point in the interior, such that convergence to this point is
uniform.