Combinatorial groupoids, cubical complexes, and the Lovasz conjecture
Combinatorics
2007-05-23 v2 Algebraic Topology
Abstract
A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. A new, holonomy-type invariant for cubical complexes is introduced, leading to a combinatorial ``Theorema Egregium'' for cubical complexes non-embeddable into cubical lattices. Parallel transport of Hom-complexes and maps is used as a tool for extending Babson-Kozlov-Lovasz graph coloring results to more general statements about non-degenerate maps (colorings) of simplicial complexes and graphs.
Cite
@article{arxiv.math/0510204,
title = {Combinatorial groupoids, cubical complexes, and the Lovasz conjecture},
author = {Rade T. Zivaljevic},
journal= {arXiv preprint arXiv:math/0510204},
year = {2007}
}