Loops with Large Twist Get Short Along Quasi-geodesics in Out(F_n)

Friday, September 21, 2018 1:30 pm - 1:30 pm EDT (GMT -04:00)
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Yulan Qing, University of Toronto

We study the behaviour of quasi-geodesics in Out(F_n) equipped with word metric. Given an element \phi in Out(F_n) there are several natural paths connecting the origin to \phi in Out(F_n). We show that these paths are, in general, not quasi-geodesics in Out(F_n).  In fact, we clear up the current misunderstanding about distance estimating in Out(F_n) by showing that there exist points in Out(F_n) where all quasi-geodesics between them backtracks in all of the current Out(F_n) complexes. 

MC 5403