Equivariant $KK$-theory for non-Hausdorff groupoids
Lachlan MacDonald
TL;DR
This paper provides a comprehensive survey of equivariant KK-theory for non-Hausdorff groupoids, adapting classical proofs and establishing new results in this generalized setting.
Contribution
It offers a detailed, unified account of equivariant KK-theory for locally Hausdorff groupoids, including proofs of results not previously documented.
Findings
Classical Kasparov product proofs extend to non-Hausdorff groupoids
New proofs for several equivariant KK-theory results
Clarification of the relationship between classical and generalized settings
Abstract
We give a detailed and unified survey of equivariant -theory over locally compact, second countable, locally Hausdorff groupoids. We indicate precisely how the "classical" proofs relating to the Kasparov product can be used almost word-for-word in this setting, and give proofs for several results which do not currently appear in the literature.
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