Combinatorial Groupoids, Cubical Complexes, and the Lovász Conjecture
نویسنده
چکیده
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 nonembeddable into cubical lattices. Parallel transport of Hom-complexes and maps is used as a tool for extending Babson-Kozlov-Lovász graph coloring results to more general statements about non-degenerate maps (colorings) of simplicial complexes and graphs.
منابع مشابه
O ct 2 00 5 Combinatorial groupoids , cubical complexes , and the Lovász conjecture
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”...
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ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 41 شماره
صفحات -
تاریخ انتشار 2009