An ascending HNN extension of a free group inside SL(2,C)
| dc.creator | Calegari, Danny | |
| dc.creator | Dunfield, Nathan M. | |
| dc.date | 2004-12-07 | |
| dc.date | 2005-06-06 | |
| dc.date.accessioned | 2026-07-07T06:33:35Z | |
| dc.date.available | 2026-07-07T06:33:35Z | |
| dc.description | We give an example of a subgroup of SL(2,C) which is a strictly ascending HNN extension of a non-abelian finitely generated free group F. In particular, we exhibit a free group F in SL(2,C) of rank 6 which is conjugate to a proper subgroup of itself. This answers positively a question of Drutu and Sapir. The main ingredient in our construction is a specific finite volume (noncompact) hyperbolic 3-manifold M which is a surface bundle over the circle. In particular, most of F comes from the fundamental group of a surface fiber. A key feature of M is that there is an element of its fundamental group with an eigenvalue which is the square root of a rational integer. We also use the Bass-Serre tree of a field with a discrete valuation to show that the group F we construct is actually free. | |
| dc.description | 7 pages. V2: minor improvements in exposition | |
| dc.identifier | https://arxiv.org/abs/math/0412136 | |
| dc.identifier | http://arxiv.org/abs/math/0412136 | |
| dc.identifier | Proc. Amer. Math. Soc. 134 (2006), no. 11, 3131-3136 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99244 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20E06; 57M | |
| dc.title | An ascending HNN extension of a free group inside SL(2,C) | |
| dc.type | text |