Delta-groupoids in knot theory

Details Delta-groupoids in knot theory Delta-groupoids in knot theory

2009-08-10

arxiv.org/abs/0908.1261v1

Mathematics

Geometric Topology

24 pages, no figures

Scientific paper

A Delta-groupoid is an algebraic structure which axiomitizes the combinatorics of a truncated tetrahedron. It is shown that there are relations of Delta-groupoids to rings, group pairs, and (ideal) triangulations of three-manifolds. In particular, one can associate a Delta-groupoid to ideal triangulations of knot complements. It is also possible to define a homology theory of Delta-groupoids. The constructions are illustrated by examples coming from knot theory.

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