Summer Conference on Topology and Its Applications

Document Type

Topology + Geometry

Publication Date


Publication Source

32nd Summer Conference on Topology and Its Applications


In this talk we will discuss some recent work on the problem of determining the extent to which the geometry of an arithmetic hyperbolic 3-manifold M is determined by the geometric genus spectrum of M (i.e., the set of isometry classes of finite area, properly immersed, totally geodesic surfaces of M, considered up to free homotopy). In particular, we will give bounds on the totally geodesic 2-systole, construct infinitely many incommensurable manifolds with the same initial geometric genus spectrum and analyze the growth of the genera of minimal surfaces across commensurability classes. These results have applications to the study of how Heegard genus grows across commensurability classes.


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