Handle additions producing essential surfaces
| dc.creator | Qiu, Ruifeng | |
| dc.creator | Wang, Shicheng | |
| dc.date | 2006-01-25 | |
| dc.date.accessioned | 2026-07-07T06:59:16Z | |
| dc.date.available | 2026-07-07T06:59:16Z | |
| dc.description | We construct a small, hyperbolic 3-manifold $M$ such that, for any integer $g\geq 2$, there are infinitely many separating slopes $r$ in $\partial M$ so that $M(r)$, the 3-manifold obtained by attaching a 2-handle to $M$ along $r$, is hyperbolic and contains an essential separating closed surface of genus $g$. The result contrasts sharply with those known finiteness results on Dehn filling, and it also contrasts sharply with the known finiteness result on handle addition for the cases $g=0,1$. Our 3-manifold $M$ is the complement of a hyperbolic, small knot in a handlebody of genus 3. | |
| dc.description | 28 pages, 22 figures | |
| dc.identifier | https://arxiv.org/abs/math/0601597 | |
| dc.identifier | http://arxiv.org/abs/math/0601597 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107683 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M10 | |
| dc.title | Handle additions producing essential surfaces | |
| dc.type | text |