On the algebraic K-theory of \({\mathbb{Z}}\) (Q1111692)

The author studies the relationships between \(K_ i{\mathbb{Z}}\), \(H_ i(St({\mathbb{Z}}),{\mathbb{Z}})\), and \(H_ i(SL({\mathbb{Z}}),{\mathbb{Z}})\) for \(i=4\), 5 \((St({\mathbb{Z}})=stabilized\) Steinberg group). He proves that the Hurewicz map \(K_ i{\mathbb{Z}}\to H_ i(St({\mathbb{Z}}))\) is an isomorphism for \(i=4\) and has a cokernel of order 2 for \(i=5\). His main tools include th Hochschild-Serre spectral sequence and an analysis of the spaces \(BSt({\mathbb{Z}})^+\), \(BSL({\mathbb{Z}})^+\) and \(BSL({\mathbb{F}}_ 3)^+\).