Rectangle condition for compression body and 2-fold branched covering

Details Rectangle condition for compression body and 2-fold branched covering Rectangle condition for compression body and 2-fold branched covering

2010-07-15

arxiv.org/abs/1007.2521v1

Mathematics

Geometric Topology

16 pages, 15 figures

Scientific paper

We give the rectangle condition for strong irreducibility of Heegaard splittings of $3$-manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of a $2$-fold covering of $S^3$ branched along a link. The condition implies that any thin meridional level surface in the link complement is incompressible. We also show that the additivity of knot width holds for a composite knot satisfying the condition.

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