[K-OS] Knot Online Seminar

[K-OS] is an online research seminar which focuses on knot theory and low-dimensional topology. Talks will be delivered by authors of recent arXiv articles that made a breakthrough in our field. It happens the 3rd Thursday of every month from 16:15 to 17:15 (CET/CEST Berlin, Brussels, Madrid, Paris, Rome, Vienna, Warsaw, Zurich) on Zoom.

It is organized by Alexandra Kjuchukova, Lukas Lewark, Delphine Moussard and Emmanuel Wagner. It benefits from logistical support from the CNRS, the university of Paris and the ETHZ.

If there is a recent arXiv preprint which you would like to see featured on the seminar, please email the organizers with your suggestion.

Forthcoming Talks

16 January 2025

• Speaker: Tye Lidman (North Carolina State University)
• Title: Cosmetic surgeries, knot complements, and Chern-Simons invariants (on 2410.21248)
• Abstract: Dehn surgery is an important construction in low-dimensional topology which turns a knot into a new three-manifold. This is deeply tied to the study of knots through their complements. The Cosmetic Surgery Conjecture predicts two different Dehn surgeries on the same knot in the three-sphere always gives different three-manifolds. We show how tools from gauge theory can help to approach this problem, settling the conjecture for almost all knots in the three-sphere. This is joint work with Ali Daemi and Mike Miller Eismeier.

20 February 2025

• Speaker: Miguel Orbegozo Rodriguez (ETH Zurich)
• Title: Homogeneous braids are visually prime (on 2408.15730)
• Abstract: For which link diagrams can we tell, simply with the 2-dimensional diagram information, whether the associated link is prime? Menasco showed that we can for alternating diagrams, and Cromwell, for positive braids. The latter further conjectured that the same would hold for any diagram for which Seifert's algorithm yields a minimal genus surface. This minimality property, if we also required that the diagram be a braid closure, is equivalent to the braid being homogeneous. Since these links are fibered, we can use open book techniques. I will present a criterion for how primeness of fibered links behaves under an operation called Murasugi sums, which we consider to be of independent interest; and explain how we can use it to prove Cromwell's conjecture for braid closures, i.e. for homogeneous braids. This is joint work with Peter Feller and Lukas Lewark.