What is … a Seifert Surface?

This page hosts information on Silvia de Toffoli's talk "What is … a Seifert Surface?" at the "What is …?" seminar. The talk will take place on Friday, December 4, 12:30pm at the BMS Loft in Urania. This talk will help you better understand the BMS Friday talk by Jack van Wijk, which will start at 2pm.

Abstract

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.

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