, Volume 317, Issue 4, pp 783-820

Annuli in generalized Heegaard splittings and degeneration of tunnel number

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract. 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 [Kw]. For example, in the absence of 2-bridge summands, the tunnel number of the sum of n knots is no less than \(\frac{2}{5}\) the sum of the tunnel numbers.

Received: 10 November 1999 / Published online: 28 June 2000