On addition of 1-handles with chart loops to 2-dimensional braids
Geometric Topology
2016-09-01 v2
Abstract
A 2-dimensional braid over an oriented surface-knot is presented by a graph called a chart on a surface diagram of . 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.
Keywords
Cite
@article{arxiv.1503.00404,
title = {On addition of 1-handles with chart loops to 2-dimensional braids},
author = {Inasa Nakamura},
journal= {arXiv preprint arXiv:1503.00404},
year = {2016}
}
Comments
30 pages, 25 figures, 3 figures added, Propositions 1.10 and 1.11 corrected, to appear in J. Knot Theory Ramifications