On the connections between the low dimensional homology groups of $\textrm{SL}_2$ and $\textrm{PSL}_2$

Behrooz Mirzaii; Elvis Torres Pérez

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arXiv · 2402.08074

On the connections between the low dimensional homology groups of $\textrm{SL}_2$ and $\textrm{PSL}_2$

Behrooz Mirzaii·Elvis Torres Pérez

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Abstract

In this article we study the low dimensional homology groups of the special linear group $\textrm{SL}_2(A)$ and the projective special linear group $\textrm{PSL}_2(A)$, $A$ a domain, through the natural surjective map $\textrm{SL}_2(A) \to \textrm{PSL}_2(A)$. In particular, we study the connection of the first, the second and the third homology groups of these groups over euclidean domains $\mathbb{Z}[\frac{1}{m}]$, $m$ a square free integer, and local domains.

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BibTeX RIS

Behrooz Mirzaii, Elvis Torres Pérez. 2024-02-12. On the connections between the low dimensional homology groups of $\textrm{SL}_2$ and $\textrm{PSL}_2$. https://arxiv.org/abs/2402.08074

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