2010/07/22 by Solie, Brent B.
#20E08 #20F65 #FOS: Mathematics #Group Theory (math.GR) #Primary 20P05 #Secondary 03D15
paper · doi:10.48550/arxiv.1007.4022
An element of a finitely generated non-Abelian free group F(X) is said to be filling if that element has positive translation length in every very small action of F(X) on an ℝ-tree. We give a proof that the set of filling elements of F(X) is exponentially F(X)-generic in the sense of Arzhantseva and Ol'shanskii. We also provide an algebraic sufficient condition for an element to be filling and show that there exists an exponentially F(X)-generic subset of filling elements whose membership problem is solvable in linear time.