Hold Date

2021-02-16 16:00〜2021-02-16 17:00

Place

IMI Auditorium (W1-D-413), West Zone 1, Ito campus, Kyushu University

Object person

　

Speaker

Hiroaki KURIHARA (Kyushu University)

Abstract:
In this talk, we study isotopy invariants of closed connected orientable surfaces in the standard $3$-sphere. Such surfaces were extensively studied by Fox, Homma, Tsukui, and Suzuki around 1950s—1970s. In their studies, $3$-manifold theory and fundamental group techniques were mainly used. In this talk, we study closed connected orientable surfaces from a viewpoint different from that of their previous studies. Such a surface splits the $3$-sphere into two compact connected orientable submanifolds. By using Heegaard splittings of the $3$-manifolds, we obtain a $2$-component handlebody-link from the original surface in the $3$-sphere. Furthermore, such a $2$-component handlebody-link is uniquely determined up to stabilizations of Heegaard splittings of the connected components of the exterior of the surface. In this talk, by using $G$-families of quandles, we construct invariants of $2$-component handlebody-links up to stabilizations. Finally, we compute our invariants for two explicit surfaces, and see that they are not equivalent.


* This seminar will be held as a dissertation hearing, but you can participate in the same way
  as a regular topology seminar.