Jan 23

Title:  Counting fixed points of pseudo-Anosov maps

Speaker: David Futer (Temple University)

Abstract: Let S be a hyperbolic surface and f a pseudo-Anosov map on S. I will describe a result that predicts the number of fixed points of f, up to constants that depend only on the surface S. If f satisfies a mild condition called “strongly irreducible,” then the logarithm of the number of fixed points of f is coarsely equal to its translation length on the Teichmuller space of S. Without this mild condition, there is still a coarse formula.

This result and its proof has some applications to the search for surface subgroups of mapping class groups, and relations between the hyperbolic volume and the knot Floer invariants of fibered hyperbolic knots. This is joint work with Tarik Aougab and Sam Taylor.