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arXiv · 2503.00909

Soft Barycentric Refinement

Oliver Knill
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Abstract

The soft Barycentric refinement preserves manifolds with or without boundary. In every dimension larger than one, there is a universal spectral central limiting measure that has affinities with the Barycentric limiting measure one dimension lower. Ricci type quantities like the length of the dual sphere of co-dimension-2 simplex stay invariant under soft refinements. We prove that the dual graphs of any manifold can be colored with 3 colors, which is in the 2-dimensional case a special case of the Groetzsch theorem. It follows that the vertices of a soft Barycentric refined q-manifold G' can be colored by q+1 or q+2 colors.

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Oliver Knill. 2025-03-02. Soft Barycentric Refinement. https://arxiv.org/abs/2503.00909

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