Seminar of Algebra

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The search for exotic knot traces

Marc Kegel (Humboldt-Universität zu Berlin)
Departamento de Álgebra
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.