On the length of knots on a Heegaard surface of a 3-manifold (Peter Feller, ETH Zürich)

23.03.2023 14:15

3-manifold theory has expanded its tool box in recent decades: topological, (Floer and quantum) homological, and geometrical methods all have been employed with success. However, often the relation between these different approaches remains mysterious.
In this talk we explore connections between the topology and the geometry of 3-manifolds by using Heegaard-splittings (topology) of a 3-manifold to describe hyperbolic structures (geometry) on it. There is no Ricci-flow machine running in the background. Instead, the motor behind what we do is an effective version of Thurston's hyperbolic Dehn surgery. Applications include a Ricci-flow free proof of Mather's result that random 3-manifolds (in the sense of Dunfield-Thurston) are hyperbolic, and bounds on the diameter and injectivity radius of a random 3-manifold.
Based on work in progress with A. Sisto and G. Viaggi.


Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Topologie et géométrie"

Organisé par

Section de mathématiques


Peter Feller, ETH Zürich

entrée libre


Catégorie: Séminaire