Rigidity of amalgamated product in negative curvature
| dc.creator | Besson, Gerard | |
| dc.creator | Courtois, Gilles | |
| dc.creator | Gallot, Sylvain | |
| dc.date | 2005-06-17 | |
| dc.date.accessioned | 2026-07-07T05:20:49Z | |
| dc.date.available | 2026-07-07T05:20:49Z | |
| dc.description | Let $Γ$ be the fundamental group of a compact n-dimensional riemannian manifold X of sectional curvature bounded above by -1. We suppose that $Γ$ is a free product of its subgroup A and B over the amalgamated subgroup C. We prove that the critical exponent $δ(C)$ of C satisfies $δ(C) \geq n-2$. The equality happens if and only if there exist an embedded compact hypersurface Y in X, totally geodesic, of constant sectional curvature -1, with fundamental group C and which separates X in two connected components whose fundamental groups are A and B. Similar results hold if $Γ$ is an HNN extension, or more generally if $Γ$ acts on a simplicial tree without fixed point. | |
| dc.identifier | https://arxiv.org/abs/math/0506350 | |
| dc.identifier | http://arxiv.org/abs/math/0506350 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75518 | |
| dc.subject | Differential Geometry | |
| dc.title | Rigidity of amalgamated product in negative curvature | |
| dc.type | text |