Seminars & Colloquia Calendar
When can you twist out exponentially growing outer automorphisms?
Edgar Bering (Temple University)
Location: Hill 005
Date & time: Tuesday, 05 February 2019 at 3:50PM - 4:50PM
Abstract: A theme in the study of mapping class groups is the construction of partial pseudo-Anosov mapping classes by various means. The oldest construction, which dates to Thurston, is to take the product of squares of two Dehn twists about curves that intersect. The resulting mapping class will be pseudo-Anosov when restricted to the subsurface filled by the curves. The study of the outer automorphism group of a free group has progressed analogously to the study of mapping class groups. In Out(F_r), the analog of a partial pseudo-Anosov mapping class is an exponentially growing outer automorphism. Using surfaces with free fundamental group, one can define Dehn twists in Out(F_r). In this talk I will present an algorithmic criterion to decide when a subgroup of Out(F_r) generated by two Dehn twists contains an exponentially growing outer automorphism, giving a complete characterization of the appropriate Out(F_r) analog of "intersection" for the analog of Thurston's construction.