A “cubist” decomposition of the Handel-Mosher axis bundle & the conjugacy problem for Out(F_r)

Tue Apr 15, 2025 4:00 p.m.—5:00 p.m.
Exterior of Sheffield-Sterling-Strathcona Hall featuring a stone carving of Yale's coat of arms and motto

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Seminar: 
Geometry & Topology

Event time: 
Tuesday, April 15, 2025 - 4:00pm

Location: 
KT 207

Speaker: 
Catherine Pfaff

Speaker affiliation: 
Institute for Advanced Study/Queen’s University

Event description: 
Outer automorphisms of free groups are largely studied via their action on Culler-Vogtmann Outer space. However, unlike in hyperbolic space or Teichmuller space (surface) settings, the dynamically minimal (fully irreducible) free group outer automorphisms act on Culler-Vogtmann Outer space with a collection of axes, whose closure is the Handel-Mosher “axis bundle.” Not much of the structure of this axis bundle has yet been understood. Together with Chi Cheuk Tsang, we prove that the axis bundle has a “cubist” structure and use this structure to find preferred axes for these outer automorphisms. We then use these axes to provide a solution to the fully irreducible conjugacy problem. This work can be seen as in analogy with that of Hamenstadt and Agol in the surface setting.