An invariant of 3-manifolds via homology cobordisms
(University of Tokyo)
Mandag 9. april 2018
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.
Kontakt: Cristiano Spotti, Martin de Borbon & Roberta Iseppi