کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4590721 1334978 2013 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A Serre–Swan theorem for bundles of bounded geometry
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A Serre–Swan theorem for bundles of bounded geometry
چکیده انگلیسی

The Serre–Swan theorem in differential geometry establishes an equivalence between the category of smooth vector bundles over a smooth compact manifold and the category of finitely generated projective modules over the unital ring of smooth functions. This theorem is here generalized to manifolds of bounded geometry. In this context it states that the category of Hilbert bundles of bounded geometry is equivalent to the category of operator ⁎-modules over the operator ⁎-algebra of continuously differentiable functions which vanish at infinity. Operator ⁎-modules are generalizations of Hilbert C⁎C⁎-modules where the category of C⁎C⁎-algebras has been replaced by a more flexible category of involutive algebras of bounded operators: The operator ⁎-algebras. Operator ⁎-modules play an important role in the study of the unbounded Kasparov product.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 265, Issue 10, 15 November 2013, Pages 2465–2499
نویسندگان
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