论文标题
对等效的分析扭转以进行适当的行动
Equivariant analytic torsion for proper actions
论文作者
论文摘要
我们构建了射线手分析扭转的模棱两可的版本，以与局部紧凑的群组在Riemannian歧管上的适当的等距作用，并具有紧凑的商。我们获得了收敛性，度量独立性，消失的均匀歧管，产品公式以及经典的射线手 - 手柄分析扭转的分解，这是对通用覆盖物上的等效扭转的共同类别的总和。我们对圆圈进行明确计算，并为$ \ operatatorName {so} _0（3,1）$的常规椭圆形元素作用，并以$ 3 $维二比的双重盈利空间作用。我们的构造和结果概括了几个早期的模棱两可分析扭转及其性质的结构，这些结构适用于有限或紧凑的群体，或对其普遍覆盖物作用的紧凑型歧管的基本组。这些早期版本的模棱两可的分析扭转与有限或紧凑的结合类别相关。我们允许在适当的生长条件下进行非划分的结合类别。
We construct an equivariant version of Ray-Singer analytic torsion for proper, isometric actions by locally compact groups on Riemannian manifolds, with compact quotients. We obtain results on convergence, metric independence, vanishing for even-dimensional manifolds, a product formula, and a decomposition of classical Ray-Singer analytic torsion as a sum over conjugacy classes of equivariant torsion on universal covers. We do explicit computations for the circle and the line acting on themselves, and for regular elliptic elements of $\operatorname{SO}_0(3,1)$ acting on $3$-dimensional hyperbolic space. Our constructions and results generalise several earlier constructions of equivariant analytic torsion and their properties, most of which apply to finite or compact groups, or to fundamental groups of compact manifolds acting on their universal covers. These earlier versions of equivariant analytic torsion were associated to finite or compact conjugacy classes; we allow noncompact conjugacy classes, under suitable growth conditions.
