Small knots and large handle additions

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dc.creatorQiu, Ruifeng
dc.creatorWang, Shicheng
dc.date2004-02-08
dc.date.accessioned2026-07-07T05:05:14Z
dc.date.available2026-07-07T05:05:14Z
dc.descriptionWe construct a hyperbolic 3-manifold $M$ (with $\partial M$ totally geodesic) which contains no essential closed surfaces, but for any even integer $g> 0$ there are infinitely many separating slopes $r$ on $\partial M$ so that $M[r]$, the 3-manifold obtained by attaching 2-handle to $M$ along $r$, contains an essential separating closed surface of genus $g$ and is still hyperbolic. The result contrasts sharply with those known finiteness results for the cases $g=0,1$. Our 3-manifold $M$ is the complement of a simple small knot in a handlebody.
dc.description25 pages, 14 figures
dc.identifierhttps://arxiv.org/abs/math/0402120
dc.identifierhttp://arxiv.org/abs/math/0402120
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70095
dc.subjectGeometric Topology
dc.subject57M10
dc.titleSmall knots and large handle additions
dc.typetext

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