A Serre-Swan Theorem for Coisotropic Algebras

Remark on the Serre-Swan theorem for non-compact manifolds

The Serre-Swan theorem provides the link between projective modules of finite rank and vector bundles over compact manifolds, and plays a prominent role in non-commutative geometry. Its extension to non-compact manifolds is discussed.

A Serre-Swan theorem for gerbe modules on étale Lie groupoids

Given a bundle gerbe on a compact smooth manifold or, more generally, on a compact étale Lie groupoid $M$, we show that the corresponding category of gerbe modules, if it is non-trivial, is equivalent to the category of finitely generated projective modules over an Azumaya algebra on $M$. This result can be seen as an equivariant Serre-Swan theorem for twisted vector bundles.

通过tepui纤维化证明一个奇异的Serre-Swan定理

A singular Serre-Swan theorem via tepui fibrations

本文通过tepui纤维化扩展了Serre-Swan定理，将有限生成C∞(M)-模作为奇异向量丛的截面，研究了奇异叶形及其结构。

A Serre-Swan theorem for bundles of bounded geometry

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…

The Serre-Swan theorem for normed modules

The aim of this note is to analyse the structure of the $L^0$-normed $L^0$-modules over a metric measure space. These are a tool that has been introduced by N. Gigli to develop a differential calculus on spaces verifying the Riemannian Curvature Dimension condition. More precisely, we discuss under which conditions an $L^0$-normed $L^0$-module can be viewed as the space of sections of a suitable measurable Banach bundle and in which sense such correspondence can be actually made into an equivalence of categories.

标准模型——交换情形：旋量、狄拉克算子与 de Rham 代数

The Standard Model - the Commutative Case: Spinors, Dirac Operator and de Rham Algebra

本文以模论方法综述经典场论的数学基础，涵盖旋量丛、狄拉克算子及 Connes 微分代数，并给出外代数丛与 Connes 微分代数同构的新证明。