We give a bound for the geometric dimension for the family of virtually cyclic groups in mapping class groups of an orientable compact surface with punctures, possibly with nonempty boundary and negative Euler characteristic. arXiv:1606.00306v3 [math.AT] 2 May 2017 fruitful conversations.
Classifying Spaces for Families
Abstract. We provide a general procedure for computing the algebraic Ktheory of finitely generated virtually free groups. The procedure describes these groups in terms of (1) the algebraic K-theory of various finite subgroups, and (2) various Farrell Nil-groups. We illustrate the process by carrying out the computation for several interesting classes of examples. The first two classes serve as a check on the method, and show that our algorithm recovers results already existing in the literature. The last two classes of examples yield new computations.
Abstract. Let Γ be a cocompact Fuchsian group. We calculate the lower algebraic K -theory of the integral group ring ZΓ and find an explicit formula for K i (ZΓ) , i ≤ 1 , in terms of the lower K -groups of maximal finite cyclic subgroups of Γ .
Mathematics Subject Classification (2000). 19A31, 19B28, 19D35.
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