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Isolated regions of a link projection

Geometric Topology 2024-10-08 v3

Abstract

A set of regions of a link projection is said to be isolated if any pair of regions in the set share no crossings. The isolate-region number of a link projection is the maximum value of the cardinality for isolated sets of regions of the link projection. In this paper, all the link projections of isolate-region number one are determined. Also, estimations for welded unknotting number and combinatorial way to find the isolate-region number are discussed, and a formula of the generating function of isolated-region sets is given for the standard projections of (2,n)(2, n)-torus links.

Keywords

Cite

@article{arxiv.2404.15818,
  title  = {Isolated regions of a link projection},
  author = {Tumpa Mahato and Ayaka Shimizu},
  journal= {arXiv preprint arXiv:2404.15818},
  year   = {2024}
}

Comments

18 pages, 14 figures