On the Algebra and Geometry of a Manifold’s Chains and Cochains
نویسندگان
چکیده
of the Dissertation On the Algebra and Geometry of a Manifold’s Chains and Cochains by Scott Owen Wilson Doctor of Philosophy in Mathematics Stony Brook University 2005 This dissertation consists of two parts, each of which describes new algebraic and geometric structures defined on chain complexes associated to a manifold. In the first part we define, on the simplicial cochains of a triangulated manifold, analogues of certain objects in differential geometry. In particular, we define a cochain product and prove several results on its convergence to the wedge product of 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 a triangulated
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Geometric Structures on the Cochains of a Manifold
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 appl...
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