Leslie Mavrakis
University of Utah
Title
Combinatorial Characterizations and Branched Manifolds
Abstract
A family F of compact n-manifolds is locally combinatorially defined (LCD) if there is a finite number of triangulated n-balls such that every manifold in F has a triangulation that locally looks like one of these n-balls. In joint work with Daryl Cooper and Priyam Patel, we show that LCD is equivalent to the existence of a compact branched n-manifold W, such that F is precisely those manifolds that immerse into W. In this way, W can be thought of as a universal branched manifold for F. In current and future work, we use this equivalence to show that, for each of the eight Thurston geometries, the family of closed 3-manifolds admitting that geometry is LCD. In this talk, I will present the main ideas of the proof of the equivalence and if time permits, construct branched 3-manifolds for a few of the geometries.