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Submanifold Projection

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Lucas Sabalka, Saint Louis University

What
  • Topology Seminar
When Fri, Feb 15, 2013
from 11:00 AM to 11:50 AM
Where Ritter Hall 316
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Abstract:  The outer automorphism group of the free group, Out(F_n), has a deep connection with the mapping class group of a surface. That connection has been fruitfully exploited to study various aspects of Out(F_n), including most recently its geometry.  One of the most useful tools for studying the geometry of the mapping class group has been the subsurface projections of Masur and Minsky. In this talk, discussing research that is joint with Dmytro Savchuk, we will discuss an analogue of subsurface projection for Out(F_n) that we call submanifold projection. Our projection is topological in nature, using intersections of embedded 2-spheres in a particular 3-manifold.  We discuss a number of desirable properties of submanifold projection, including a Behrstock inequality and a Bounded Geodesic Image theorem.

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