# The topological 4-genus and forbidden minor characterisations

## Topologie

Lieu:
Salle Duhem M3
Orateur:
Livio Liechti
Affiliation:
Université Pierre et Marie Curie
Dates:
Vendredi, 6 Avril, 2018 - 14:00 - 15:00
Résumé:

Famously, a finite graph is planar exactly if it does not admit two specific graphs as minors. In fact, a characterisation by finitely many forbidden minors exists for any property which passes to minors with respect to a well-quasi-order. In this context, we discuss a minor relation for Seifert surfaces embedded in three-space, defined by isotopy into an incompressible subsurface, and the property to have an equality between the ordinary Seifert genus and the topological 4-genus of the boundary knot. In particular, we characterise this equality in the case of positive braid knots.