Yuta NOZAKI
An invariant of 3-manifolds via homology cobordisms
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.