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Tuesday Seminar on Topology
Seminar information archive ～04/09｜Next seminar｜Future seminars 04/10～
| Date, time & place | Tuesday 16:00 - 17:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | IKE Yuichi, KONNO Hokuto, SAKASAI Takuya |
2018/01/23
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Yuta Nozaki (The University of Tokyo)
An invariant of 3-manifolds via homology cobordisms (JAPANESE)
Yuta Nozaki (The University of Tokyo)
An invariant of 3-manifolds via homology cobordisms (JAPANESE)
[ Abstract ]
For a closed 3-manifold X, we consider the 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.
For a closed 3-manifold X, we consider the 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.
