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Further to Grothendieck's works that proof that we have a Riemann-Roch theorem for certain morphisms of algebraic varieties and of Hirzebruch and Atiyah for certain morphisms of differentiable manifolds, we will proof that we have a Riemann-Roch theorem for continuous applications between compact spaces verifying certain conditions, in the context of topological K-theory of compact spaces.The Riemann-Roch theorem that we have in mind involves the K functor defined by K (X) :=-1K°(X) K (X), where K°(X) denotes the Grothendieck group of complex fiber bundles over X,-1 where K (X) := K°(S(X)),…mehr

Produktbeschreibung
Further to Grothendieck's works that proof that we have a Riemann-Roch theorem for certain morphisms of algebraic varieties and of Hirzebruch and Atiyah for certain morphisms of differentiable manifolds, we will proof that we have a Riemann-Roch theorem for continuous applications between compact spaces verifying certain conditions, in the context of topological K-theory of compact spaces.The Riemann-Roch theorem that we have in mind involves the K functor defined by K (X) :=-1K°(X) K (X), where K°(X) denotes the Grothendieck group of complex fiber bundles over X,-1 where K (X) := K°(S(X)), where S(X) denotes the reduced suspension of X and the H_ functor k defined by par H_(X) := H (X ;Q) .These two functors will apply to the category where the objects are compact spaces and the morphisms are applications that we will call, using Lang and Fulton terminology, regular.
Autorenporträt
Laurent Motais de Narbonne is the author of several works. He currently holds the position of Manager at Softeam Cadextan.