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arXiv · 2107.13915

The third homology of $SL_{2}$ of real quadratically closed fields

Rodrigo Cuitun Coronado
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Abstract

For a real closed field $\mathbf{R}$, we use the theory of the refined Bloch group to give a new short proof of the isomorphisms $H_{3}(SL_{2}(\mathbf{R}),\mathbb{Z})\cong K_{3}^{\mathrm{ind}}(\mathbf{R})$ and $H_{3}(SL_{n}(\mathbf{R}),\mathbb{Z})\cong H_{3}(SL_{2}(\mathbf{R}),\mathbb{Z})\oplus K_{3}^{M}(\mathbf{R})^{0}$ for $n\geq3$.

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Rodrigo Cuitun Coronado. 2021-07-29. The third homology of $SL_{2}$ of real quadratically closed fields. https://arxiv.org/abs/2107.13915

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