On addition of 1-handles with chart loops to 2-dimensional braids

Abstract

A 2-dimensional braid over an oriented surface-knot $F$ is presented by a graph called a chart on a surface diagram of $F$. We consider 2-dimensional braids obtained by an addition of 1-handles equipped with chart loops. We introduce moves of 1-handles with chart loops, called 1-handle moves, and we investigate how much we can simplify a 2-dimensional braid by using 1-handle moves. Further, we show that an addition of 1-handles with chart loops is an unbraiding operation.

30 pages, 25 figures, 3 figures added, Propositions 1.10 and 1.11 corrected, to appear in J. Knot Theory Ramifications

References in corpus (3)

• Surface links which are coverings over the standard torus
• Satellites of an oriented surface link and their local moves
• Cords and 1-handles attached to surface-knots

Cited by in corpus (1)

• Branched covering surface-knots with degree three have the simplifying numbers less than three