Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An equivariant orbifold index for proper actions   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.

12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg