Computations of quandle cocyle invariants of surface-links using marked graph diagrams
Geometric Topology
2015-02-06 v1
Abstract
By using the cohomology theory of quandles, quandle cocycle invariants and shadow quandle cocycle invariants are defined for oriented links and surface-links via broken surface diagrams. By using symmetric quandles, symmetric quandle cocycle invariants are also defined for unoriented links and surface-links via broken surface diagrams. A marked graph diagram is a link diagram possibly with -valent vertices equipped with markers. S. J. Lomonaco, Jr. and K. Yoshikawa introduced a method of describing surface-links by using marked graph diagrams. In this paper, we give interpretations of these quandle cocycle invariants in terms of marked graph diagrams, and introduce a method of computing them from marked graph diagrams.
Keywords
Cite
@article{arxiv.1502.01450,
title = {Computations of quandle cocyle invariants of surface-links using marked graph diagrams},
author = {Seiichi Kamada and Jieon Kim and Sang Youl Lee},
journal= {arXiv preprint arXiv:1502.01450},
year = {2015}
}
Comments
40 pages, 29 figures