Bibliographic Details
| Title: |
Surface subgroups from linear programming |
| Authors: |
Calegari, Danny, Walker, Alden |
| Source: |
Duke Math. J. 164, no. 5 (2015), 933-972 |
| Publication Year: |
2012 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Group Theory, Mathematics - Dynamical Systems, Mathematics - Geometric Topology |
| More Details: |
We show that certain classes of graphs of free groups contain surface subgroups, including groups with positive $b_2$ obtained by doubling free groups along collections of subgroups, and groups obtained by "random" ascending HNN extensions of free groups. A special case is the HNN extension associated to the endomorphism of a rank 2 free group sending a to ab and b to ba; this example (and the random examples) answer in the negative well-known questions of Sapir. We further show that the unit ball in the Gromov norm (in dimension 2) of a double of a free group along a collection of subgroups is a finite-sided rational polyhedron, and that every rational class is virtually represented by an extremal surface subgroup. These results are obtained by a mixture of combinatorial, geometric, and linear programming techniques.
Comment: version 2; 30 pages, 16 figures. This version abridged for publication; for applications to counting quasimorphisms and flat surfaces see version 1 |
| Document Type: |
Working Paper |
| DOI: |
10.1215/00127094-2877511 |
| Access URL: |
http://arxiv.org/abs/1212.2618 |
| Accession Number: |
edsarx.1212.2618 |
| Database: |
arXiv |
