Iterated Grafting and Holonomy Lifts of Teichmueller space
| dc.creator | Hensel, Sebastian W. | |
| dc.date | 2008-02-22 | |
| dc.date | 2008-12-15 | |
| dc.date.accessioned | 2026-07-07T12:12:15Z | |
| dc.date.available | 2026-07-07T12:12:15Z | |
| dc.description | Let $X$ be a closed hyperbolic surface and $λ, η$ be weighted geodesic multicurves which are short on X. We show that the iterated grafting along $λ$ and $η$ is close in the Teichmueller metric to grafting along a single multicurve which can be given explicitly in terms of $λ$ and $η$. Using this result, we study the holonomy lifts $gr_λρ_{X,λ}$ of Teichmueller geodesics $ρ_{X,λ}$ for integral laminations $λ$ and show that all of them have bounded Teichmueller distance to the geodesic $ρ_{X,λ}$. We obtain analogous results for grafting rays. Finally we consider the asymptotic behaviour of iterated grafting sequences $\gr_{nλ}X$ and show that they converge geometrically to a punctured surface. | |
| dc.description | Major rewrite. Extended all of the results to multicurves and included a much more detailed treatment of holonomy lifts of both grafting rays and Teichmueller geodesics. 39 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/0802.3290 | |
| dc.identifier | http://arxiv.org/abs/0802.3290 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210487 | |
| dc.subject | Differential Geometry | |
| dc.subject | 51M10, 30F60 | |
| dc.title | Iterated Grafting and Holonomy Lifts of Teichmueller space | |
| dc.type | text |