$\vec{w}h\alpha\mathfrak{t}\;\; i\mathbb{S}\ldots$

a Seifert surface?


Who?
Silvia de Toffoli (TU Berlin)
When?
2009/12/04, 12:30
Before the BMS Friday Colloquium by Prof. Jan van Wijk.
Where?
Urania Berlin, at the BMS Loft (2nd floor)
About what?

Giving the basic definitions and explaining the some important ideas, we will introduce the field of knot theory. We will explain the relation between a knot and its diagram and how to find invariants which allow us to distinguish different knots (or links). Thanks to an easy invariant we will prove the existence of non-trivial knots! We will introduce the concept of Seifert Surface of a knot: An orientable, compact connected surface whose boundary is the knot. We will show an algorithm to create a Seifert Surface starting form an arbitrary projection of a knot. We will see that this algorithm will be useful to calculate the genus, a knot invariant, of a certain class of knots. If time will permit we will talk of the signature of a knot, its relation with the unknotting number (Gordian distance), and the general context in which Seifert was working when he introduced his surface.