Speaker:
Marc Kegel (Humboldt-Universität zu Berlin)
Email:
kegelmarc87@gmail.comLocation:
Departamento de Álgebra
Date:
Fri, 3 mar 2023 12:30
Marc Kegel got his Ph.D. in 2017 at the University of Cologne under the supervision of Prof. Hansjörg Geiges. Since 2018 he is employed as guest lecturer at the Humboldt-University of Berlin. His research is mainly in low-dimensional topology and contact geometry.
Every knot leaves a trace in the 4-dimensional world. The trace of a knot is the smooth $4$-manifold obtained by attaching a $2$-handle to the $4$-ball along a knot in the $3$-sphere. We will carefully introduce the relevant notions and discuss a recent strategy due to Manolesu-Piccirillo to disprove the smooth Poincar\'e conjecture by finding knot traces with certain exotic properties. In the second part of the talk, we will explain a method to search for such exotic knot traces, as indicated in the picture. This is based on joint work in progress with Nicolas Weiss.