论文标题
一个模棱两可的Orbifold索引，用于适当的动作
An equivariant orbifold index for proper actions
论文作者
论文摘要
对于$ h $ compact的局部紧凑型组的适当的，共同的动作，我们定义了一个$ h \ times g $ - equivariant索引$ h $ h $ transversally-transversally-transversally-transverically-transverically-transveric enlipticalliptic运算符，该索引的值为$ kk _*（c^*h，c^*g）$。这同时概括了鲍姆 - 康涅狄格州的分析装配图，atiyah的横向椭圆操作员索引和川崎的orbifold索引。该索引还将装配图概括为Orbifolds上的椭圆运算符。在有问题的歧管是一个真正的半谎言组的特殊情况下，$ g $是一个共同的晶格，$ h $是最大的紧凑型亚组，我们意识到connes的狄拉克感应图 - 卡斯帕罗夫（Kasparov）作为kasparov产品，是卡斯帕洛夫（Kasparov）的产品，并获得了Spin-Dirac Operators in Comparacters promplactermecles sypemalles somplectalles sypermectermectermemermetrectermectermectermectermectim s的索引。
For a proper, cocompact action by a locally compact group of the form $H \times G$, with $H$ compact, we define an $H \times G$-equivariant index of $H$-transversally elliptic operators, which takes values in $KK_*(C^*H, C^*G)$. This simultaneously generalises the Baum--Connes analytic assembly map, Atiyah's index of transversally elliptic operators, and Kawasaki's orbifold index. This index also generalises the assembly map to elliptic operators on orbifolds. In the special case where the manifold in question is a real semisimple Lie group, $G$ is a cocompact lattice and $H$ is a maximal compact subgroup, we realise the Dirac induction map from the Connes--Kasparov conjecture as a Kasparov product and obtain an index theorem for Spin-Dirac operators on compact locally symmetric spaces.
