Immersed surfaces and Dehn surgery
| dc.creator | Wu, Ying-Qing | |
| dc.date | 1999-12-06 | |
| dc.date.accessioned | 2026-07-07T05:32:09Z | |
| dc.date.available | 2026-07-07T05:32:09Z | |
| dc.description | Let $F$ be a proper essential immersed surface in a hyperbolic 3-manifold $M$ with boundary disjoint from a torus boundary component $T$ of $M$. Let $α$ be the set of coannular slopes of $F$ on $T$. The main theorem of the paper shows that there is a constant $K$ and a finite set of slopes $Λ$ on $T$, such that if $β$ is a slope on $T$ with $Δ(β, α_i) > K$ for all $α_i$ in $α$, and $β$ is not in $Λ$, then $F$ remains incompressible after Dehn filling on $T$ along the slope $β$. In certain sense, this means that $F$ survives most Dehn fillings. The proof uses minimal surface theory, integral of differential forms, and properties of geometrically finite groups. As a consequence of our method, it will also be shown that Freedman tubings of immersed geometrically finite surfaces are essential if the tubes are long enough. | |
| dc.description | 29 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/9912049 | |
| dc.identifier | http://arxiv.org/abs/math/9912049 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79557 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N10 | |
| dc.title | Immersed surfaces and Dehn surgery | |
| dc.type | text |