Student 3-Manifold Seminar: The Sphere Theorem

Seminar | February 15 | 4-5:30 p.m. | 939 Evans Hall

 Kyle Miller, UC Berkeley

 Department of Mathematics

A version of the Papakyriakopoulos Sphere Theorem states that a compact $3$-manifold with nontrivial $\pi _2$ has a two-sided embedded sphere or projective plane representing a nontrivial homotopy class. We will discuss ends of groups and how the theorem follows from Stallings's theorem on finitely generated groups with more than one end.