Abstract: The Thurston norm is a norm on the second homology of a hyperbolic 3-manifold which, given a homology class, returns the minimal complexity over all surfaces representing the class. The unit ball for this norm is a polyhedron symmetric about the origin, and by understanding the surfaces representing the vertices of this polyhedron one gets a wealth of information about the embedded surfaces in the manifold. In 2008, Cooper and Tillmann gave an algorithm for computing the Thurston norm ball of a closed manifold, using normal surfaces. After discussing the relevant background, I will discuss an adaptation of their techniques to the case of cusped hyperbolic 3-manifolds by using spun normal surfaces. Finally, I will conclude with an interactive demonstration of a computer program available from https://pypi.org/project/tnorm/ that implements this algorithm. This is joint work with Daryl Cooper and Stephan Tillmann.
To add/edit talks, please log in on the department web page, then return to Announce. Alternatively if you know the Announce
username/password, click the link below: