English

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 FF is presented by a graph called a chart on a surface diagram of FF. 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