Aarhus University Seal / Aarhus Universitets segl

QGM seminar by Yuta Nozaki (University of Tokyo)

Title: An invariant of 3-manifolds via homology cobordisms

2018.04.06 | Jane Jamshidi

Date Mon 09 Apr
Time 16:15 17:15
Location 1532-322 (Øv.G3.3)


For a closed 3-manifold X, we consider a topological invariant defined as the minimal integer g such that X is obtained as the closure of a homology cobordism over a surface of genus g. We prove that the invariant equals one for every lens space, which is contrast to the fact that some lens spaces do not admit any open book decomposition whose page is a surface of genus one. The proof is based on the Chebotarev density theorem and binary quadratic forms in number theory.