Algebraic K-theory of groups wreath product with finite groups

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• 作者：S.K. Roushon
• 关键词：Fibered isomorphism conjecture ; 3-Manifold groups ; Discrete subgroup of Lie group ; Poly- groups ; Braid groups
• 刊名：Topology and its Applications
• 出版年：2007
• 出版时间：1 May 2007
• 年：2007
• 卷：154
• 期：9
• 页码：1921-1930
• 全文大小：152 K

文摘

The Farrell–Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example, for discrete subgroups of Lie groups [F.T. Farrell, L.E. Jones, Isomorphism conjectures in algebraic K-theory, J. Amer. Math. Soc. 6 (1993) 249–297], virtually poly-infinite cyclic groups [F.T. Farrell, L.E. Jones, Isomorphism conjectures in algebraic K-theory, J. Amer. Math. Soc. 6 (1993) 249–297], Artin braid groups [F.T. Farrell, S.K. Roushon, The Whitehead groups of braid groups vanish, Internat. Math. Res. Notices 10 (2000) 515–526], a class of virtually poly-surface groups [S.K. Roushon, The isomorphism conjecture for 3-manifold groups and K-theory of virtually poly-surface groups, math.KT/0408243, K-Theory, in press] and virtually solvable linear group [F.T. Farrell, P.A. Linnell, K-Theory of solvable groups, Proc. London Math. Soc. (3) 87 (2003) 309–336]. We extend these results in the sense that if G is a group from the above classes then we prove the conjecture for the wreath product GH for H a finite group. The need for this kind of extension is already evident in [F.T. Farrell, S.K. Roushon, The Whitehead groups of braid groups vanish, Internat. Math. Res. Notices 10 (2000) 515–526; S.K. Roushon, The Farrell–Jones isomorphism conjecture for 3-manifold groups, math.KT/0405211, K-Theory, in press; S.K. Roushon, The isomorphism conjecture for 3-manifold groups and K-theory of virtually poly-surface groups, math.KT/0408243, K-Theory, in press]. We also prove the conjecture for some other classes of groups.