Student 3-Manifold Seminar: The loop theorem and Dehn's lemma

Seminar | February 8 | 4-5:30 p.m. | 939 Evans Hall

 Kyle Miller, UC Berkeley

 Department of Mathematics

Simplified, the loop theorem states that if the induced map $\pi _1(\partial M)\to \pi _1(M)$ for a $3$-manifold $M$ is not injective, then there is a nullhomotopy of an essential loop in $\partial M$ that can be represented by an embedded disk. We will go through the proof of Stalling's formulation of the loop theorem using Papakyriakopoulos's tower construction and discuss some applications.