Combinatorial Approximation to the Divergence of One-Forms on Surfaces


Lieven Smits

Bibliographical Reference

Israel Journal of Mathematics, volume 75 (1991), pages 257-271.


We consider the approximation of a differential operator on forms by combinatorial objects via the correspondences of Whitney and de Rham. We prove that the Hilbert space dual of the combinatorial coboundary is an L2 approximation to the codifferential of one-forms on a two-dimensional Riemannian manifold.


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  1. Albeverio, Sergio and Zegarlinski, Boguslaw, Construction of Convergent Simplicial Approximations of Quantum Fields on Riemannian Manifolds, University of Bochum preprint SFB 237, 1989.
  2. Cheeger, J., Analytic Torsion and Reidemeister Torsion, Proc. Nat. Acad. Sci. USA 74 (1977), 2651-2654.
  3. Cheeger, J., Müller, W. and Schrader, Robert, On the Curvature of Piecewise Flat Spaces, Comm. Math. Phys. 92 (1984), 405-454.
  4. de Rham, Georges, "Variétés différentiables," Hermann, Paris 1960.
  5. Dodziuk, Józef, Finite-difference Approach to the Hodge Theory of Harmonic Forms, Amer. J. Math. 98 (1976), 79-104.
  6. Dodziuk, Józef, and Patodi, Vijay Kumar, Riemannian Structures and Triangulations of Manifolds, J. Indian Math. Soc. 40 (1976), 1-52.
  7. Eckmann, B., Harmonische Funktionen und Randwertaufgaben in einem Komplex, Comment. Math. Helv. 17 (1945), 240-255.
  8. Müller, W., Analytic Torsion and R-torsion of Riemannian Manifolds, Adv. Math. 28 (1978), 233-305.
  9. Whitney, Hassler, "Geometric Integration Theory," Princeton University Press, Princeton 1957.

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