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A functorial equivariant K-theory spectrum and an equivariant Lefschetz formula

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arxiv 1104.3441 v1 pith:S4ZQZ6OT submitted 2011-04-18 math.KT

Ivo Dell'Ambrogio , Heath Emerson , Tamaz Kandelaki , Ralf Meyer This is my paper · ORCID
classification math.KT
keywords equivariantspectrumformulafunctorialk-theorylefschetztracesadditivity
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We construct a symmetric spectrum representing the G-equivariant K-theory of C*-algebras for a compact group or a proper groupoid G. Our spectrum is functorial for equivariant *-homomorphisms. We use this to establish the additivity of the canonical traces for endomorphisms of strongly dualisable objects in the bootstrap class in equivariant KK, in analogy to previous results for traces in stable homotopy theory. As an application, we prove an equivariant analogue of the Lefschetz trace formula for Hodgkin Lie groups.

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  1. Groups with Spanier-Whitehead duality

    math.KT 2019-08 conditional novelty 6.0 of 10

    For groups with a gamma element, Spanier-Whitehead K-duality holds exactly when the strong Baum-Connes conjecture holds, and all a-T-menable groups with a G-compact model of EG satisfy this duality.

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