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edit approved Jul 25, 2014 at 5:37
Drew Heard
edit approved Jul 25, 2014 at 5:37
Drew Heard
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K $K$-homology of BG$BG$

Let G$G$ be a finite group. Atiyah proved that the K$K$-cohomology of BG$BG$ vanishes in odd degrees and in even degrees is the completion of the representation ring of G$G$ at the augmentation ideal.

What is the K$K$-homology of BG$BG$? I mean the stable homotopy groups of the complex K$K$-theory spectrum smash BG$BG$.

K-homology of BG

Let G be a finite group. Atiyah proved that the K-cohomology of BG vanishes in odd degrees and in even degrees is the completion of the representation ring of G at the augmentation ideal.

What is the K-homology of BG? I mean the stable homotopy groups of the complex K-theory spectrum smash BG.

$K$-homology of $BG$

Let $G$ be a finite group. Atiyah proved that the $K$-cohomology of $BG$ vanishes in odd degrees and in even degrees is the completion of the representation ring of $G$ at the augmentation ideal.

What is the $K$-homology of $BG$? I mean the stable homotopy groups of the complex $K$-theory spectrum smash $BG$.

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KHBG
KHBG
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K-homology of BG

Let G be a finite group. Atiyah proved that the K-cohomology of BG vanishes in odd degrees and in even degrees is the completion of the representation ring of G at the augmentation ideal.

What is the K-homology of BG? I mean the stable homotopy groups of the complex K-theory spectrum smash BG.