ncku-talk2023-12-21

Colloquium

DATE 2023-12-21　15:10-16:00

PLACE 數學系館 1F3174教室

SPEAKER 王以晟教授（國立中山大學應用數學系）

TITLE Slice an Aapple, and Glue the Pieces Back Together?

ABSTRACT In this talk, we consider the application of the JSJ decomposition to handlebody-knot theory. The JSJ decomposition decomposes a 3-manifold into simple pieces by cutting along some specially chosen annuli and tori. It turns out that, in the case of genus one and two handlebody-knots, the pieces in the decomposition are rather restricted and can be classified into finitely many types. On the other hand, how to glue these simple pieces back to recover the knot is a complex issue. The talk hopes to give a quick introduction to how the decomposition works, and how it is used to classify handlebody-knots, and how the gluing information may be recorded. I will also give some outline on the current classification program in this direction and some unsolved problems in this area.

Colloquium

DATE	2023-12-21　15:10-16:00

PLACE	數學系館 1F3174教室

SPEAKER	王以晟教授（國立中山大學應用數學系）

TITLE	Slice an Aapple, and Glue the Pieces Back Together?

ABSTRACT	In this talk, we consider the application of the JSJ decomposition to handlebody-knot theory. The JSJ decomposition decomposes a 3-manifold into simple pieces by cutting along some specially chosen annuli and tori. It turns out that, in the case of genus one and two handlebody-knots, the pieces in the decomposition are rather restricted and can be classified into finitely many types. On the other hand, how to glue these simple pieces back to recover the knot is a complex issue. The talk hopes to give a quick introduction to how the decomposition works, and how it is used to classify handlebody-knots, and how the gluing information may be recorded. I will also give some outline on the current classification program in this direction and some unsolved problems in this area.