Mapping Class Groups and Interpolating Complexes: Rank

Details Mapping Class Groups and Interpolating Complexes: Rank Mapping Class Groups and Interpolating Complexes: Rank

2007-06-19

arxiv.org/abs/0706.2740v2

J. Ramanujan Math. Soc. 24, No.4 (2009) 341-357

Mathematics

Geometric Topology

v2 Final version incorporating refree comments 16pgs no figs

Scientific paper

A family of interpolating graphs $\calC (S, \xi)$ of complexity $\xi$ is constructed for a surface $S$ and $-2 \leq \xi \leq \xi (S)$. For $\xi = -2, -1, \xi (S) -1$ these specialise to graphs quasi-isometric to the marking graph, the pants graph and the curve graph respectively. We generalise Theorems of Brock-Farb and Behrstock-Minsky to show that the rank of $\calC (S, \xi)$ is $r_\xi$, the largest number of disjoint copies of subsurfaces of complexity greater than $\xi $ that may be embedded in $S$. The interpolating graphs $\calC (S, \xi)$ interpolate between the pants graph and the curve graph.

Affiliated with

Also associated with

No associations

Rating

Mapping Class Groups and Interpolating Complexes: Rank does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mapping Class Groups and Interpolating Complexes: Rank, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mapping Class Groups and Interpolating Complexes: Rank will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-281406