K_4(Z) is the trivial group, by John Rognes

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) previously constructed by the author, and a group homology computation of H_1(SL_4(Z); St_4) by C. Soulé (see 0268), to compute the odd primary spectrum homology of K(Z) in degrees < 5. This shows that the odd torsion in K_4(Z) is trivial. The 2-torsion in K_4(Z) was shown to be trivial by the author and Weibel.

John Rognes <rognes@math.uio.no>