Simplifying branched covering surface-knots by chart moves involving black vertices
Abstract
A branched covering surface-knot is a surface-knot in the form of a branched covering over an oriented surface-knot , where we include the case when the covering has no branch points. A branched covering surface-knot is presented by a graph called a chart on a surface diagram of . We can simplify a branched covering surface-knot by an addition of 1-handles with chart loops to a form such that its chart is the union of free edges and 1-handles with chart loops. We investigate properties of such simplifications for the case when branched covering surface-knots have a non-zero number of branch points, using chart moves involving black vertices.
Keywords
Cite
@article{arxiv.1709.07762,
title = {Simplifying branched covering surface-knots by chart moves involving black vertices},
author = {Inasa Nakamura},
journal= {arXiv preprint arXiv:1709.07762},
year = {2018}
}
Comments
19 pages, 15 figures, minor modifications, to appear in Illinois Journal of Mathematics. arXiv admin note: text overlap with arXiv:1707.07888