论文标题
在适当的lie groupoid的卷积代数的Hochschild同源性上
On the Hochschild homology of convolution algebras of proper Lie groupoids
论文作者
论文摘要
我们通过在轨道的空间上引入卷积纸条，研究适当的lie群体卷积代数的Hochschild同源性。 We develop a localization result for the associated Hochschild homology sheaf, and prove that the Hochschild homology sheaf at each stalk is quasi-isomorphic to the stalk at the origin of the Hochschild homology of the convolution algebra of its linearization, which is the transformation groupoid of a linear action of a compact isotropy group on a vector space.然后，我们解释了Brylinski的Ansatz，以计算紧凑型组对多种作用的转化组的Hochschild同源性。我们验证了Brylinski的猜想，以表明Hochschild同源性由相关惯性空间上的基本相对形式给出。
We study the Hochschild homology of the convolution algebra of a proper Lie groupoid by introducing a convolution sheaf over the space of orbits. We develop a localization result for the associated Hochschild homology sheaf, and prove that the Hochschild homology sheaf at each stalk is quasi-isomorphic to the stalk at the origin of the Hochschild homology of the convolution algebra of its linearization, which is the transformation groupoid of a linear action of a compact isotropy group on a vector space. We then explain Brylinski's ansatz to compute the Hochschild homology of the transformation groupoid of a compact group action on a manifold. We verify Brylinski's conjecture for the case of smooth circle actions that the Hochschild homology is given by basic relative forms on the associated inertia space.
