Geometric Structures on the Cochains of a Manifold

Scott O. Wilson

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Geometric Structures on the Cochains of a Manifold

Scott O. Wilson

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Abstract

In this paper we develop several algebraic structures on the simplicial cochains of a triangulated manifold that are analogues of objects in differential geometry. We study a cochain product and prove several statements about its convergence to the wedge product on differential forms. Also, for cochains with an inner product, we define a combinatorial Hodge star operator, and describe some applications, including a combinatorial period matrix for surfaces. We show that for a particularly nice cochain inner product, these combinatorial structures converge to their continuum analogues as the mesh of a triangulation tends to zero.

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BibTeX RIS

Scott O. Wilson. 2005-05-11. Geometric Structures on the Cochains of a Manifold. https://arxiv.org/abs/math/0505227

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