Stephan Tillman

(Joint work with Stefan Friedl) The Thurston norm of a 3-manifold measures the minimal complexity of surfaces representing a given homology class. We will show how in most (possibly all cases) one can use Fox calculus to easily calculate the unit ball of the Thurston norm if the fundamental group has at most two generators. The main ingredients are marked polytopes, which generalise the Bieri-Neumann-Strebel invariant, a group theoretic analogue of the Thurston norm, and a link between Fox derivatives and genealised Novikov rings.