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

Daniel Juan-Pineda; Luis Jorge S\'anchez Salda\~na

arxiv: 1511.02767 · v1 · pith:RZIS734Xnew · submitted 2015-11-09 · 🧮 math.KT · math.GT

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

Daniel Juan-Pineda , Luis Jorge S\'anchez Salda\~na This is my paper

classification 🧮 math.KT math.GT

keywords groupsalgebraictheorygrouphyperbolicranksclassesexplicit

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

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