We consider the classical problem of a position of n-dimensional manifold Mⁿ in . We show that we can define the fundamental (n+1)-cycle and the shadow fundamental (n+2)-cycle for a fundamental quandle of a knotting . In particular, we show that for any fixed quandle, quandle coloring, and shadow quandle coloring, of a diagram of Mⁿ embedded in we have (n+1)- and (n+2)-(co)cycle invariants (i.e. invariant under Roseman moves).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-11,
author = {J\'ozef H. Przytycki and Witold Rosicki},
title = {Cocycle invariants of codimension 2 embeddings of manifolds},
journal = {Banach Center Publications},
volume = {102},
year = {2014},
pages = {251-289},
zbl = {1312.57031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-11}
}
Józef H. Przytycki; Witold Rosicki. Cocycle invariants of codimension 2 embeddings of manifolds. Banach Center Publications, Tome 102 (2014) pp. 251-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-11/