分野別セミナー

In this talk, we explain that the virtual dimension $d$ of the Seiberg--Witten moduli space satisfies $d\leq 2r(p-1)-2$ if the Seiberg--Witten invariant is not divisible by $p^r$ and some topological conditions are satisfied. For the proof, we employ Buaer--Furuta's cohomotopy refinement of the Seiberg--Witten invariant. By using techniques in hard homotopy theory such as Toda brackets, the divisibility of the Seiberg--Witten invariant is deduced. This talk is based on a joint work with Tsuyoshi Kato, Daisuke Kishimoto and Kouichi Yasui.