LDT seminar 2021

HYU - Low Dimensional Topology Seminar

Kim, Jaehoon KAIST 2022.02.25 , 16:00

2-complexes with unique embedding in 3-space

A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove a 3-dimensional analogue: a simply-connected 2-complex every link graph of which is 3-connected admits an essentially unique locally flat embedding into the 3-sphere, if it admits one at all. This can be thought of as a generalisation of the 3-dimensional Schoenflies theorem. This is joint work with Agelos Georgakopoulos.

2021 Winter Workshop (2021.12.27 - 29)

Lee , Sang yop 중앙대 2021.01.20 , 14:00 (zoom)

Inequivalent handlebody-knots with homeomorphic complements

We distinguish the handlebody-knots 5_1,6_4 and 5_2,6_13 in the table, due to Ishii et al, of irreducible handlebody-knots up to six crossings. Furthermore, we construct two infinite families of handlebody-knots, each containing one of the pairs 5_1,6_4 and 5_2,6_13, and show that any two handlebody-knots in each family have homeomorphic complements but they are not equivalent.

An, Byung Hee 경북대 2021.01.21 , 22 & 02.04 13:30 (zoom)

Legendrian graphs and ruling polynomial

In this series of lectures, we will talk about Legendrian graphs in the standard contact three space and their invariants. In particular, we will consider the ruling invariant of Legendrian graphs and discuss how it is related with the other invariants such as Thurston-Bennequin number and Kauffman polynomial.

The main theme of each lecture is as follows:

Lecture 1. Legendrian graphs and their invariants

Lecture 2. Ruling polynomials for Legendrian graphs

Lecture 3. More on Ruling polynomials for Legendrian graphs

References

Oh, Seungsang 고려대 2021.01.25, 13:30 (zoom)

Tilings of Euclidean space by Knotted Tiles

We give several kinds of tilings of regular solids, $B^{3}$ and $S^{3}$, by knotted solid tori or handlebodies all of which are congruent and nontrivially linked. We also present higher dimensional tilings of $B^{p+3}$ by congruent regular neighborhoods of any $p$-spun knot.