March 30: Seifert Surfaces and Knot Genus by Alex Teeter

Abstract:

Knot Theory, a field of mathematics born from a misguided model for atoms, has since grown to become an important subfield of Topology. Not only does it have much of mathematical interest, but also numerous connections to fields such as graph theory, the study of manifolds, and applications to Biology and Physics. We will analyze the connection between Knot Theory and the Topology of Surfaces. Along the way, we will cover the Euler Characteristic, Genus and the beautiful Classification Theorem of Surfaces. Through this consideration, we develop an algorithm to associate each Knot with a surface, and uncover an important invariant, the Genus of a Knot. This will not only allow us to distinguish between different Knots, but will also be vital in establishing fundamental properties of prime and composite Knots. No prior background in Knot Theory or Topology is assumed.

#MTBoS #topology #knots #surfaces #seifert

[d.]

this is such an incredibly helpful presentation, tysm