Conway products and links with multiple bridge surfaces

Details Conway products and links with multiple bridge surfaces Conway products and links with multiple bridge surfaces

2006-08-16

arxiv.org/abs/math/0608435v1

Mathematics

Geometric Topology

29 pages, 19 figures

Scientific paper

Suppose a link K in a 3-manifold M is in bridge position with respect to two different bridge surfaces P and Q, both of which are c-weakly incompressible in the complement of K. Then either P and Q can be properly isotoped to intersect in a nonempty collection of curves that are essential (including non-meridional) on both surfaces, or K is a Conway product with respect to an incompressible Conway sphere that naturally decomposes both P and Q into bridge surfaces for the respective factor link(s).

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