Abstract
We prove that the fourth algebraic K-group of the integers is the trivial group, i.e., that K 4( Z)=0 . The argument uses rank-, poset- and component filtrations of the algebraic K-theory spectrum K( Z) from Rognes (Topology 31 (1992) 813–845; K-Theory 7 (1993) 175–200), and a group homology computation of H 1(SL 4( Z); St 4) from Soulé, to compute the odd primary spectrum homology of K( Z) in degrees ⩽4. This shows that the odd torsion in K 4( Z) is trivial. The 2-torsion in K 4( Z) was shown to be trivial in Rognes and Weibel (J. Amer. Math. Soc., to appear).
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