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Extended Regge complex for linearized Riemann-Cartan geometry and cohomology

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arxiv 2312.11709 v1 pith:RSY4QZ3U submitted 2023-12-18 math.NA cs.NAmath-phmath.DGmath.MP

Snorre H. Christiansen , Kaibo Hu , Ting Lin This is my paper
classification math.NAcs.NAmath-phmath.DGmath.MP
keywords cohomologycomplexlinearizedgeometrymathcalreggerhamriemann-cartan
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abstract

We show that the cohomology of the Regge complex in three dimensions is isomorphic to $\mathcal{H}^{{\scriptscriptstyle \bullet}}_{dR}(\Omega)\otimes\mathcal{RM}$, the infinitesimal-rigid-body-motion-valued de~Rham cohomology. Based on an observation that the twisted de~Rham complex extends the elasticity (Riemannian deformation) complex to the linearized version of coframes, connection 1-forms, curvature and Cartan's torsion, we construct a discrete version of linearized Riemann-Cartan geometry on any triangulation and determine its cohomology.

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  1. Convergence of Finite Element Methods for Ricci Flow

    math.NA 2026-07 conditional novelty 8.0 of 10

    A Regge/Lagrange finite element discretization of the 2D Ricci flow converges with O(h^{q+1}+h^{r+1}) error in the metric and Gaussian curvature.

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