### Classical knot invariants and slice surfaces by Peter Feller

- Series
- Geometry Topology Seminar Pre-talk
- Time
- Wednesday, April 3, 2019 - 12:45 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Peter Feller – ETH Zurich – peter.feller@math.ethz.ch

In the setup of classical knot theory---the study of embeddings of the circle into S^3---we recall two examples of classical knot invariants: the Alexander polynomial and the Seifert form.

We then introduce notions from knot-concordance theory, which is concerned with the study of slice surfaces of a knot K---surfaces embedded in the 4-ball B^4 with boundary the knot K. We will comment on the difference between the smooth and topological theory with a focus on a surprising feature of the topological theory: classical invariants govern the existence of slice surfaces of low genus in a way that is not the case in the smooth theory. This can be understood as an analogue of a dichotomy in the study of smooth and topological 4-manifolds.