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Disk presentations of surface-knots and -links
by
Shin Satoh
Chiba University
We introduce a new way of presenting surface-knots and -links in R4, called disk presentation. This enables us to define the disk index Δ(F) of a surface-knot or -link F. We prove that Δ(F)=2 if and only if F is a trivial S2-knot, and Δ(F)=3 if and only if F is a trivial non-orientable surface-knot with |e(F)| £ 3−χ(F), where e(F) is the normal Euler number of F and χ(F) is the Euler characteristic of F.
Date received: February 7, 2005
Copyright © 2005 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 # capo-25.