Bounded degeneration of tunnel number
by
Jennifer Schultens
Emory University
Coauthors: Martin Scharlemann

Tunnel number has been shown to behave quite erratically under the operation of connected sum of knots. We will provide examples of this erratic behaviour and show that one can nevertheless give bounds for degeneration of tunnel number. In particular, the tunnel number of the connected sum of two prime knots is bounded below by 2/5 the sum of the tunnel numbers of the knots if neither knot is 2-bridge, and by 1/3 the sum of the tunnel numbers in any case.

Preprint: Annuli in generalized Heegaard splittings and degeneration of tunnel number

Date received: February 7, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-27.