Handle additions producing essential surfaces

Details Handle additions producing essential surfaces Handle additions producing essential surfaces

2006-01-25

arxiv.org/abs/math/0601597v1

Mathematics

Geometric Topology

28 pages, 22 figures

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Handle additions producing essential surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Handle additions producing essential surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Handle additions producing essential surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-404907