GGT seminar: Growth of Essential Surfaces via Measured Laminations
- Sponsor
- Groups, Geometry, and Topology Seminar
- Speaker
- Brevan Ellefsen
- Views
- 35
- Originating Calendar
- Mathematics Seminar Series: Groups, Geometry, and Topology
Due to the work of Thurston, Rivin, and Mirzakhani, it is known that the count of essential curves in a compact surface S of geodesic length at most n grows like n^d, where d is the dimension of the space of measured laminations on S (equivalently, the Teichmuller space of S).
Recent work of Dunfield, Garoufalidis, and Rubenstein showed the count of essential multi-surfaces of Euler characteristic –2n in a sufficiently nice 3-manifold M grows like n^d, where d is described in terms of normal surfaces associated to specific triangulation of M. In analogy with the 2-dimensional picture, the authors conjectured that d should be the dimension of an associated space of measured laminations.
The measured lamination space of a 3-manifold M was first defined by Hatcher in the 1980s, but unlike its 2-dimensional counterpart has remained rather obscure. In this talk we will recount foundational ideas about the measured lamination space, and will discuss how they lead to a resolution of the aforementioned conjecture.