Discreteness Criteria and the Hyperbolic Geometry of Palindroms
| dc.creator | Gilman, Jane | |
| dc.creator | Keen, Linda | |
| dc.date | 2008-08-26 | |
| dc.date.accessioned | 2026-07-07T09:58:28Z | |
| dc.date.available | 2026-07-07T09:58:28Z | |
| dc.description | We consider non-elementary representations of two generator free groups in $PSL(2,\mathbb{C})$, not necessarily discrete or free, $G = < A, B >$. A word in $A$ and $B$, $W(A,B)$, is a palindrome if it reads the same forwards and backwards. A word in a free group is {\sl primitive} if it is part of a minimal generating set. Primitive elements of the free group on two generators can be identified with the positive rational numbers. We study the geometry of palindromes and the action of $G$ in $\HH^3$ whether or not $G$ is discrete. We show that there is a {\sl core geodesic} $Ł$ in the convex hull of the limit set of $G$ and use it to prove three results: the first is that there are well defined maps from the non-negative rationals and from the primitive elements to $Ł$; the second is that $G$ is geometrically finite if and only if the axis of every non-parabolic palindromic word in $G$ intersects $Ł$ in a compact interval; the third is a description of the relation of the pleating locus of the convex hull boundary to the core geodesic and to palindromic elements. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0808.3488 | |
| dc.identifier | http://arxiv.org/abs/0808.3488 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167726 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 30F40, 32G15, 30F60, 51M10, 57M99 | |
| dc.title | Discreteness Criteria and the Hyperbolic Geometry of Palindroms | |
| dc.type | text |