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 -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).
