Virtually geometric words and Whitehead's algorithm

Abstract

Motivated by a question of Gordon and Wilton, we consider the question of which collections of words are "virtually geometric". In particular, we prove that some words (e.g. bbaaccabc) are not virtually geometric.

9 pages, 2 figures. (v2) Corrected statement of Theorem 2.4, and rewrote Remark 1.5 slightly (v3) Some improvements to the exposition and expansion of some remarks suggested by the referee