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arXiv · 1511.02767

On the ranks of the algebraic $K$-Theory of hyperbolic groups

Daniel Juan-Pineda·Luis Jorge Sánchez Saldaña
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Abstract

Let $G$ be a word hyperbolic group. We prove that the algebraic $K$-theory groups of $\dbZ [G]$, $K_n(\dbZ[G])$, have finite rank for all $n\in \dbZ$. For a few classes of groups, we give explicit formulas for the ranks of the algebraic $K$-theory groups of their group rings.

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Daniel Juan-Pineda, Luis Jorge Sánchez Saldaña. 2015-11-09. On the ranks of the algebraic $K$-Theory of hyperbolic groups. https://arxiv.org/abs/1511.02767

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