51吃瓜网

Title: A "cubist" decomposition of the Handel-Mosher axis bundle

Abstract: In joint work with Chi Cheuk Tsang, we show that the axis bundle of a nongeometric fully irreducible outer automorphism admits a canonical 鈥渃ubist鈥� decomposition into branched cubes that fit together with special combinatorics. From this structure, we locate a canonical finite collection of periodic fold lines in each axis bundle. This can be considered as an analogue of results of Hamenstadt and Agol from the surface setting, which state that the set of trivalent train tracks carrying the unstable lamination of a pseudo-Anosov map can be given the structure of a CAT(0) cube complex, and that there is a canonical periodic fold line in this cube complex. This work also gives a 鈥渉ands on鈥� solution to the fully irreducible conjugacy problem in Out(F_r), and an answer to questions of Handel-Mosher and Bridson-Vogtmann regarding the geometry of the axis bundle.

We will gather for teatime in the lounge at 4pm after the talk.

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