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Marco Marengon: Unraveling the mystery of the Conway knot

2022.10.26. - 2022.10.26.
Rényi Institute, Main Lecture Hall


15.15-16.00: Reception

16.00-16.45: Introductory talk by Stefan Mihajlović: How to get around a 4-manifold?

Abstract: I will introduce manifolds and explain how to build them from building blocks that we call handles. After that, our focus will be on manifolds of dimension 4 - how handles look in this concrete setting, and what moves we can do to change the handle decomposition. Followed by intuitive explanations of 4-dimensional moves, I will try to emphasize diagrammatic 3-dimensional pictures which show how topologists usually work with 4-manifolds hands-on.

17.00-18.00: Main lecture

Abstract: The study of mathematical knots, i.e. the embeddings of a circle in a 3-dimensional space, is a very active area of topology. More than 50 years ago, in 1970, Conway studied the knot 11n34 (, now known as the Conway knot. The question of whether the Conway knot bounds a disc when a fourth dimension is allowed has a deep connection with some of the most fundamental open problems in 4-dimensional topology. For several decades this question remained impenetrable, until in 2018 a short and elegant argument of Piccirillo showed that the answer is “no”.

In the talk I will discuss the precise formulation of the question, its importance for 4-dimensional topology, and I will sketch Piccirillo’s proof.


Marco Marengon