Adapting the subdivision theorem for mock bundles in the case of geometric cocycles, we prove the independence of orientations and subdivisions for geometric cohomology groups.A subdivision theorem for simplicial algebraic cocycles and an alternative description of the subdivision of a geometric cocycle are derived.A duality map between cohomology and homology of a cycle K is then introduced: this map is proved to be, if K is an oriented manifold, the Poincarè duality isomorphism.
Subdivision and Poincaré duality / Grasselli, Luigi. - In: RIVISTA DI MATEMATICA DELLA UNIVERSITÀ DI PARMA. - ISSN 0035-6298. - STAMPA. - 9:(1983), pp. 95-103.
Subdivision and Poincaré duality
GRASSELLI, Luigi
1983
Abstract
Adapting the subdivision theorem for mock bundles in the case of geometric cocycles, we prove the independence of orientations and subdivisions for geometric cohomology groups.A subdivision theorem for simplicial algebraic cocycles and an alternative description of the subdivision of a geometric cocycle are derived.A duality map between cohomology and homology of a cycle K is then introduced: this map is proved to be, if K is an oriented manifold, the Poincarè duality isomorphism.Pubblicazioni consigliate
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