A Generalization of the Prime Geodesic Theorem to Counting Conjugacy Classes of Free Subgroups
| dc.creator | Bowen, Lewis | |
| dc.date | 2006-06-07 | |
| dc.date | 2006-10-01 | |
| dc.date.accessioned | 2026-07-07T07:17:02Z | |
| dc.date.available | 2026-07-07T07:17:02Z | |
| dc.description | The classical prime geodesic theorem (PGT) gives an asymptotic formula (as $x$ tends to infinity) for the number of closed geodesics with length at most $x$ on a hyperbolic manifold $M$. Closed geodesics correspond to conjugacy classes of $π_1(M)=Γ$ where $Γ$ is a lattice in $G=SO(n,1)$. The theorem can be rephrased in the following format. Let $X(\Z,Γ)$ be the space of representations of $\Z$ into $Γ$ modulo conjugation by $Γ$. $X(\Z,G)$ is defined similarly. Let $π: X(\Z,Γ)\to X(\Z,G)$ be the projection map. The PGT provides a volume form $vol$ on $X(\Z,G)$ such that for sequences of subsets $\{B_t\}$, $B_t \subset X(\Z,G)$ satisfying certain explicit hypotheses, $|π^{-1}(B_t)|$ is asymptotic to $vol(B_t)$. We prove a statement having a similar format in which $\Z$ is replaced by a free group of finite rank under the additional hypothesis that $n=2$ or 3. | |
| dc.description | 32 pages, 5 figures. This is the second version. The introduction has been expanded and two new examples inserted | |
| dc.identifier | https://arxiv.org/abs/math/0606162 | |
| dc.identifier | http://arxiv.org/abs/math/0606162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113798 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20E09, 20F69, 37E35, 51M10 | |
| dc.title | A Generalization of the Prime Geodesic Theorem to Counting Conjugacy Classes of Free Subgroups | |
| dc.type | text |