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Cocykle invariants of codimension 2 embeddings of manifolds
by
Witold Rosicki
University of Gdansk
Coauthors: J.H.Przytycki

Cocykle invariants of codimension 2 embeddings of manifolds

Witold Rosicki and Józef H. Przytycki

We consider the classical problem of a position of n-dimensional manifold Mⁿ in \Kr 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 knotting Mⁿ → \Kr 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 \Kr R ⁿ⁺² we have (n+1)- and (n+2)-(co)cycle invariants (i.e.invariant under Roseman moves).

The case n=2 is well known. The case n=3 we can explane in a geometric way. The general case we described in arXiv:1310.3030v1 .

Date received: December 8, 2014

Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbjz-44.