Geometric realisation of degeneration of hyperbolic structures on 3-manifolds
Event details
| Date | 17.03.2016 |
| Hour | 13:00 › 14:00 |
| Speaker | Ohshika, Ken'ichi (Osaka) |
| Location |
Bât. MA, MA12
|
| Category | Conferences - Seminars |
Abstract: Degeneration of hyperbolic structures on a surface can be described by points in the Thurston boundary of Teichmuller space.
We can also interpret this by using isometric actions of the fundamental group of the surface on R-trees and their dual laminations, whose existence is guaranteed by Skora’s theorem.
We can consider the same kind of description for degeneration of hyperbolic structures on the interior of a compact 3-manifold with boundary.
In this case however, in general it is impossible to realise R-tree actions coming from degeneration by dual codimension-one laminations.
I will give concrete examples of R-tree actions which cannot be realised by dual laminations, and show that in the case of boundary-irreducible manifolds, it is possible to realise R-tree actions by dual codimension-one laminations which lie in 3-manifolds homotopy equivalent to the original one.
We can also interpret this by using isometric actions of the fundamental group of the surface on R-trees and their dual laminations, whose existence is guaranteed by Skora’s theorem.
We can consider the same kind of description for degeneration of hyperbolic structures on the interior of a compact 3-manifold with boundary.
In this case however, in general it is impossible to realise R-tree actions coming from degeneration by dual codimension-one laminations.
I will give concrete examples of R-tree actions which cannot be realised by dual laminations, and show that in the case of boundary-irreducible manifolds, it is possible to realise R-tree actions by dual codimension-one laminations which lie in 3-manifolds homotopy equivalent to the original one.
Practical information
- Informed public
- Free
Organizer
- Marc Troyanov
Contact
- Marc Troyanov