Cocycle invariants of codimension 2 embeddings of manifolds
Volume 103 / 2014
Banach Center Publications 103 (2014), 251-289
MSC: 57Q45, 57M25.
DOI: 10.4064/bc103-0-11
Abstract
We consider the classical problem of a position of $n$-dimensional manifold $M^{n}$ in $\mathbb R^{n+2}$. 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 $M^n \to \mathbb R^{n+2}$. In particular, we show that for any fixed quandle, quandle coloring, and shadow quandle coloring, of a diagram of $M^n$ embedded in $\mathbb R^{n+2}$ we have $(n+1)$- and $(n+2)$-(co)cycle invariants (i.e. invariant under Roseman moves).
