Nonadditivity of the Seifert Genus for Virtual Knots (Killian Davis, Ohio State University)

19.03.2026 14:15

Abstract: Classically, the Seifert genus for knots respects knot addition, leading to useful structural theorems, such as the fact that genus 1 knots are prime. For virtual knots, however, this is false. In this talk, we will demonstrate nonadditivity of the Seifert genus by showing two unknots which add to a genus 1 virtual knot. We will also introduce the main tool used to prove this: the homotopy Zh construction.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Topologie et
géométrie"

entrée libre