| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
28 March 2024 |
|
| | | |
|
Article forum
| |
|
Immersed surfaces and Dehn surgery | Ying-Qing Wu
; | Date: |
6 Dec 1999 | Subject: | Geometric Topology MSC-class: 57N10 | math.GT | Abstract: | 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 $alpha$ 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 $Lambda$ on $T$, such that if $eta$ is a slope on $T$ with $Delta(eta, alpha_i) > K$ for all $alpha_i$ in $alpha$, and $eta$ is not in $Lambda$, then $F$ remains incompressible after Dehn filling on $T$ along the slope $eta$. 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. | Source: | arXiv, math.GT/9912049 | Services: | Forum | Review | PDF | Favorites |
|
|
No message found in this article forum.
You have a question or message about this article?
Ask the community and write a message in the forum.
If you want to rate this article, please use the review section..
To add a message in the forum, you need to login or register first. (free): registration page
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |