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On the tunnel number and the cutting number of handlebody-knots
by
Tomo Murao
University of Tsukuba
For a handlebody-knot H, a constituent handlebody-knot of H is a handlebody-knot obtained from H by removing an open regular neighborhood of some meridian disks of H. In this talk, we provide necessary conditions to be constituent handlebody-knots by using G-family of quandles colorings. Furthermore, as the corollaries, we give lower bounds for the tunnel number and the cutting number of handlebody-knots, which are dual geometric invariants for handlebody-knots.
Date received: December 30, 2018
Copyright © 2018 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbpq-36.