Abstract
Let or . Let and be the pure and the full braid groups of respectively. If is any of these groups, we show that satisfies the Farrell–Jones Fibered Isomorphism Conjecture and use this fact to compute the lower algebraic –theory of the integral group ring , for . The main results are that for , the Whitehead group of , and vanish for and . For , the Whitehead group of vanishes for all , vanishes for all except for the cases and vanishes for all .
Citation
Daniel Juan-Pineda. Silvia Millan-López. "The Whitehead group and the lower algebraic $K$–theory of braid groups on $\mathbb{S}^2$ and $\mathbb{R}P^2$." Algebr. Geom. Topol. 10 (4) 1887 - 1903, 2010. https://doi.org/10.2140/agt.2010.10.1887
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