Quid seminar

par Mme Alice Merz (Université de Lille, laboratoire Paul Painlevé)

mercredi 26 mars 2025, 18:00 → 19:15 Europe/Paris

129 Room Picard (IMT 1R2)

Title:

Slice knots and exotic R^4's

 

Abstract:

 

Knots are a fundamental tool to understand 3- and 4-dimensional topology. A particularly relevant class of knots, having close connection to 4-manifolds topology, is the one of slice knots. These knots were first defined by Fox and Milnor in 1958, and constitute still nowadays a very important field of research. 

In this talk I will give an introduction to some fundamental concepts in knot theory, highlighting some differences between the 3-dimensional and the 4-dimensional settings and focusing on the concept of slice knots. As an application, I will show a construction due to Gompf to build exotic R^4's, i.e. manifolds homeomorphic but not diffeomorphic to R^4.