 

Catherine Pfaff
Ideal Whitehead graphs in Out(F_{r}). I. Some unachieved graphs view print


Published: 
June 20, 2015 
Keywords: 
Outer automorphism, free group, fully irreducible, ideal Whitehead graph 
Subject: 
20F65 


Abstract
Masur and Smillie, 1993, proved precisely which singularity index lists arise from pseudoAnosov mapping classes. In search of an analogous theorem for outer automorphisms of free groups, Handel and Mosher, 2011, ask: Is each connected, simplicial, (2r1)vertex graph the ideal Whitehead graph of a fully irreducible ϕ ∈ Out(F_{r})? We answer this question in the negative by exhibiting, for each r, examples of connected (2r1)vertex graphs that are not the ideal Whitehead graph of any fully irreducible ϕ ∈ Out(F_{r}). In the course of our proof we also develop machinery used in Pfaff, 2012, to fully answer the question in the rankthree case.


Author information
Department of Mathematics, University of California, Santa Barbara, CA 931063080
catherine.pfaff@gmail.com

