The Seifert volume of 3-manifolds
We will explain how gauge theory may be used to compute the volume of representations of 3-manifold groups into the Lie group G defined as the isometry group of the universal covering of SL(2,R).
As an application we solve, for 3-manifolds, the following questions raised by Gromov in the early 80s: for which n-manifolds N is the set of degrees of maps f:M-->N finite for any n-manifold M?
This is joint work with Shisheng Wang.