Cocycle invariants of codimension 2 embeddings of manifolds

Józef H. Przytycki, and Witold Rosicki. "Cocycle invariants of codimension 2 embeddings of manifolds." Banach Center Publications 103.1 (2014): 251-289. <http://eudml.org/doc/286429>.

@article{JózefH2014,
abstract = {We consider the classical problem of a position of n-dimensional manifold Mⁿ in $ℝ^\{n+2\}$. 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 $Mⁿ → ℝ^\{n+2\}$. In particular, we show that for any fixed quandle, quandle coloring, and shadow quandle coloring, of a diagram of Mⁿ embedded in $ℝ^\{n+2\}$ we have (n+1)- and (n+2)-(co)cycle invariants (i.e. invariant under Roseman moves).},
author = {Józef H. Przytycki, Witold Rosicki},
journal = {Banach Center Publications},
keywords = {higher dimensional knot; rack; quandle; fundamental quandle; quandle coloring; quandle cocycle invariant},
language = {eng},
number = {1},
pages = {251-289},
title = {Cocycle invariants of codimension 2 embeddings of manifolds},
url = {http://eudml.org/doc/286429},
volume = {103},
year = {2014},
}

TY - JOUR
AU - Józef H. Przytycki
AU - Witold Rosicki
TI - Cocycle invariants of codimension 2 embeddings of manifolds
JO - Banach Center Publications
PY - 2014
VL - 103
IS - 1
SP - 251
EP - 289
AB - We consider the classical problem of a position of n-dimensional manifold Mⁿ in $ℝ^{n+2}$. 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 $Mⁿ → ℝ^{n+2}$. In particular, we show that for any fixed quandle, quandle coloring, and shadow quandle coloring, of a diagram of Mⁿ embedded in $ℝ^{n+2}$ we have (n+1)- and (n+2)-(co)cycle invariants (i.e. invariant under Roseman moves).
LA - eng
KW - higher dimensional knot; rack; quandle; fundamental quandle; quandle coloring; quandle cocycle invariant
UR - http://eudml.org/doc/286429
ER -