Covers and curve complex

By Kasra Rafi, Saul Schleimer. 2007

57 citations recorded by the source corpus.

We provide the first nontrivial examples of quasi-isometric embeddings between curve complexes; these are induced by orbifold covers. This leads to new quasi-isometric embeddings between mapping class groups. As a corollary, in the mapping class group normalizers of finite subgroups are undistorted.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b410aacb58e4da7ca792c9c6fc0cddfb73f4439b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Joseph Maher
2. Saul Schleimer
3. H. Masur
4. Matt Clay
5. Kasra Rafi
6. U. Hamenstaedt
7. Alessandro Sisto
8. Samuel J. Taylor

In Mathematical Physics

1. Saul Schleimer
2. Joseph Maher
3. H. Masur
4. Matt Clay
5. Kasra Rafi
6. A. Zorich
7. Dawei Chen
8. G. Forni

Citations in the corpus

• The geometry of the disk complex (2010, background): “The inductive partition is closely linked with the hierarchy machine [31] and with the notion of antichains introduced in [42].”
• Uniform hyperbolicity of the curve graph via surgery sequences (2013, background): “2 of [18], the curve complex C((1))(S) isometrically embeds in the curve complex C((1))(Σ).”
• Random walks on the mapping class group (2006, background): “along the geodesic. This means that the map from C(O) to C(Σ) is a quasiconvex embedding, so the convex hull of fix1(H) is contained in a bounded 16 neighbourhood of fix1(H). In fact, Rafi and Schleimer [RS09] have shown that this map is a quasiisometric embedding. We now show that dC(x,fix6δ(h)) 6 K3dC”