Elsevier

Journal of Algebra

Volume 570, 15 March 2021, Pages 366-396
Journal of Algebra

The third homology of SL2(Q)

https://doi.org/10.1016/j.jalgebra.2020.12.006Get rights and content
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Abstract

We calculate the structure of H3(SL2(Q),Z[12]). Let H3(SL2(Q),Z)0 denote the kernel of the (split) surjective homomorphism H3(SL2(Q),Z)K3ind(Q). Each prime number p determines an operator p on H3(SL2(Q),Z) with square the identity. We prove that H3(SL2(Q),Z[12])0 is the direct sum of the (1)-eigenspaces of these operators. The (1)-eigenspace of p is the scissors congruence group, over Z[12], of the field Fp, which is a cyclic group whose order is the odd part of p+1.

MSC

19G99
20G10

Keywords

K-theory
Group homology

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