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I have a doubt.

Borel computed the rank of the higher algebraic k-theory of $\mathbb{Z}$:

$rank(K_n)(\mathbb{Z})= 1$ if $n\equiv1 mod4$, otherwise this rank is equal to 0.

On the other hand Bjorn Jahren proved for any finite group $G$ that

$rank(K_n(\mathbb{Z}[G]))=c$ if $n\equiv3 mod4$, where c is the number of irreductible complex representation of G.

If I let $G=1$, then I have that $rank(K_n)(\mathbb{Z})= 1$ if $n\equiv3 mod4$...

this is a contradiction with Borel's result. What happened here? Am I wrong? (I hope so)

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    $\begingroup$ Maybe you have misunderstood the statement and $c$ is the number of complex representations that are not real. $\endgroup$
    – Tom Goodwillie
    Commented Apr 24, 2012 at 22:24
  • $\begingroup$ A very naive mistake I think. Thank you $\endgroup$
    – Luis Jorge
    Commented Apr 24, 2012 at 22:41

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