Sign up or sign in

Geometric Group Theory

Paige Hillen (virtual)

Subevent of Geometric Group Theory - Thurs. PM

Forbes 2070E

Eastern Time (US & Canada)

Starts at: 2025-03-06 03:35PM

Ends at: 2025-03-06 03:55PM

Latent symmetry of graphs and stretch factors in Out(Fn)

Paige Hillen ⟨paigehillen@ucsb.edu⟩

Abstract:

Given an irreducible element of Out($F_n$), there is a graph and an irreducible “train track map” on this graph, which induces the outer automorphism on the fundamental group. The stretch factor of an outer automorphism measures the asymptotic growth rate of words in $F_n$ under applications of the automorphism, and appears as the leading eigenvalue of the transition matrix of such a train track representative. I’ll present work showing a lower bound for the stretch factor in terms of the number of edges in the graph and the number of folds in the fold decomposition of the train track map. Moreover, in certain cases, a notion of the latent symmetry of a graph G gives a lower bound on the number of folds required for any irreducible train track map on G. I’ll use this to classify all single fold train track maps.

Back to events