ar X iv : m at h - ph / 0 60 10 15 v 1 9 J an 2 00 6 DIFFERENTIAL COMPLEXES AND EXTERIOR CALCULUS
نویسنده
چکیده
In this paper we present a new theory of exterior calculus over k-dimensional domains in a smooth n-manifold, unifying the discrete and continuum theories. The discrete theory carries a full set of classical operators, products, and relations of calculus and geometry and is free from the standard problems encountered in other theories of discrete exterior calculus. It is based on the Koszul complex, and converges to the smooth continuum with respect to a norm on the space of " pointed chains " , culminating in the chainlet complex. Through this complex, we discover a broad theory of coordinate free, multivector analysis in smooth manifolds for which the classical smooth theory becomes a special case. It applies equally well to simplicial complexes, bilayer structures (e.g., soap films) and nonsmooth domains. [H5]. " The introduction of numbers as coordinates ... is an act of violence " – Philosophy of Mathematics and Natural Science, 1949. Hermann Weyl.
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تاریخ انتشار 2006