Every surface is a leaf

Series
Geometry Topology Student Seminar
Time
Wednesday, May 6, 2020 - 2:00pm for 1 hour (actually 50 minutes)
Location
Online
Speaker
Justin Lanier – Georgia Tech – jlanier8@gatech.edu
Organizer
Hongyi Zhou

Every closed 3-manifold admits foliations, where the leaves are surfaces. For a given 3-manifold, which surfaces can appear as leaves? Kerékjártó and Richards gave a classification up to homeomorphism of noncompact surfaces, which includes surfaces with infinite genus and infinitely many punctures. In their 1985 paper "Every surface is a leaf", Cantwell--Conlon prove that for every orientable noncompact surface L and every closed 3-manifold M, M has a foliation where L appears as a leaf. We will discuss their paper and construction and the surrounding context.