Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661308 | Topology and its Applications | 2007 | 23 Pages |
Abstract
In this paper we develop several algebraic structures on the simplicial cochains of a triangulated manifold and prove they converge to their differential-geometric analogues as the triangulation becomes small. The first such result is for a cochain cup product converging to the wedge product on differential forms. Moreover, we show any extension of this product to a Cā-algebra also converges to the wedge product of forms. For cochains equipped with an inner product, we define a combinatorial star operator and show that for a certain cochain inner product this operator converges to the smooth Hodge star operator.
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Physical Sciences and Engineering
Mathematics
Geometry and Topology