Annuli in generalized Heegaard splittings and degeneration of tunnel number

Details Annuli in generalized Heegaard splittings and degeneration of tunnel number Annuli in generalized Heegaard splittings and degeneration of tunnel number

1999-03-12

arxiv.org/abs/math/9903078v1

Mathematics

Geometric Topology

12 figures, 40 pages, including an appendix by Andrew Casson

Scientific paper

We analyze how a family of essential annuli in a compact 3-manifold will induce, from a strongly irreducible generalized Heegaard splitting of the ambient manifold, generalized Heegaard splittings of the complementary components. There are specific applications to the subadditivity of tunnel number of knots, improving somewhat bounds of Kowng. For example, in the absence of 2-bridge summands, the tunnel number of the sum of n knots is no less than 2/5 the sum of the tunnel numbers.

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