Graduate Geometry, Topology and Dynamics Seminar
Edgar A. Bering IV
UIC
2+1=3 but not uniquely
Abstract: Last week we (morally) showed that the only way to obtain a 3-manifold from a 2-manifold and a 1-manifold is to fiber over the circle.
This week I will review the results that we proved, and apply them to the case of a closed 3-manifold whose fundamental group is a non-trivial direct product.
Following the philosophy of last week's presentation we get the answer we expect, namely $M=F_g\times S^1$ for some closed surface $F_g$. However, the resulting circle
bundle structure is far from unique; we have $F_{n(g-1)+1} \to M \to S^1$ for every $n > 0$. The remainder of the talk will discuss both algebraic and geometric constructions
of the many bundle structures.
Wednesday April 9, 2014 at 3:00 PM in SEO 612