Jacob Rasmussen : Minimal genus surfaces in 3 and 4 dimensions

Posted by , part of the Departmental Colloquium.

At

Nov. 19, 2010, 3 p.m.

In

SEO 636

Abstract

Given a smooth manifold $M$ and a primitive homology class $x \in H_2(M)$, what is the minimal genus of a smoothly embedded surface representing $x$? I'll discuss what we know about this question, and describe applications to topology in dimension three (understanding knots with lens spaces surgeries) and four (constructing exotic $\mathbb R^4$'s).