deRham’s Theorem for Simplicial Complexes
This chapter begins with a definition of the piecewise linear rational polynomial forms on a simplicial complex. These are shown to compute the usual rational singular cohomology (the p.l. deRham theorem). The construction is shown to be natural under subdivision of the simplicial complex and to produce a multiplicative isomorphism to singular cohomology. Connections with the usual smooth deRham theorem are given using piecewise smooth forms on a smoothly triangulated manifold.
KeywordsSimplicial Complex Short Exact Sequence Polynomial Form Differential Algebra Cochain Complex
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