Geometric Analysis and Topology Seminar

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Algebraic Degrees of Pseudo-Anosov Stretch Factors

Speaker: Balazs Strenner, IAS

Location: Warren Weaver Hall 517

Date: Friday, April 29, 2016, 11 a.m.

Synopsis:

Consider a mapping of the torus that stretches and compresses it in two directions. (These are called Anosov maps.) The lift of such a map to the universal cover is the action of a matrix in SL(2,Z) on the plane and the stretch factor is an eigenvalue of the matrix. Therefore only quadratic algebraic integers can be stretch factors of the torus. For higher genus surfaces, the topology of the surface still imposes constraints on the possible algebraic degrees of the stretch factors, but now a wider variety of degrees may appear. In this talk, I will explain a construction that realizes stretch factors of all possible degrees.