Third Year Candidacy Requirement: "Extending Holonomy Representations by HNN Extensions"

Speaker: Jeffrey Norton, Washington University in Saint Louis

Abstract: In 1958 Milnor proved a result about flat connections that would eventually become a foundational result for the field of foliations. In 1971 Wood applied Milnor’s techniques to circle bundles to establish a classification of foliations transverse to the circle fibers in terms of representations of the fundamental group of the base space of the circle bundle. In 1981 Eisenbud, Hirsch, and Neumann applied Wood’s techniques to classify some foliations in three-manifolds, which are almost circle bundles, in terms of representations of the fundamental group of the three-manifold. Recent developments and conjectures in the field of foliations suggest there may yet be another step to take in this direction. We’ll discuss what that step might look like. 

Host: Rachel Roberts