ترغب بنشر مسار تعليمي؟ اضغط هنا

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

204   0   0.0 ( 0 )
 نشر من قبل Christoph Schweigert
 تاريخ النشر 2014
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Given a bundle gerbe on a compact smooth manifold or, more generally, on a compact etale 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.



قيم البحث

اقرأ أيضاً

We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the the fixed point case (known as Zungs theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passing to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise conditions needed for the theorem to hold (which often have been misstated in the literature).
In this paper, we introduce the notion of a topological groupoid extension and relate it to the already existing notion of a gerbe over a topological stack. We further study the properties of a gerbe over a Serre, Hurewicz stack.
Let $mathcal{G}$ be a Lie groupoid. The category $Bmathcal{G}$ of principal $mathcal{G}$-bundles defines a differentiable stack. On the other hand, given a differentiable stack $mathcal{D}$, there exists a Lie groupoid $mathcal{H}$ such that $Bmathca l{H}$ is isomorphic to $mathcal{D}$. Define a gerbe over a stack as a morphism of stacks $Fcolon mathcal{D}rightarrow mathcal{C}$, such that $F$ and the diagonal map $Delta_Fcolon mathcal{D}rightarrow mathcal{D}times_{mathcal{C}}mathcal{D}$ are epimorphisms. This paper explores the relationship between a gerbe defined above and a Morita equivalence class of a Lie groupoid extension.
Let $mathbb{X}=[X_1rightrightarrows X_0]$ be a Lie groupoid equipped with a connection, given by a smooth distribution $mathcal{H} subset T X_1$ transversal to the fibers of the source map. Under the assumption that the distribution $mathcal{H}$ is i ntegrable, we define a version of de Rham cohomology for the pair $(mathbb{X}, mathcal{H})$, and we study connections on principal $G$-bundles over $(mathbb{X}, mathcal{H})$ in terms of the associated Atiyah sequence of vector bundles. We also discuss associated constructions for differentiable stacks. Finally, we develop the corresponding Chern-Weil theory and describe characteristic classes of principal $G$-bundles over a pair $(mathbb{X}, mathcal{H})$.
We give a concise introduction to (discrete) algebras arising from etale groupoids, (aka Steinberg algebras) and describe their close relationship with groupoid C*-algebras. Their connection to partial group rings via inverse semigroups also explored.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا