The $K$-theoretic Farrell-Jones conjecture for CAT(0)-groups
نویسندگان
چکیده
منابع مشابه
The K-theoretic Farrell-jones Conjecture for Hyperbolic Groups
We prove the K-theoretic Farrell-Jones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.
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Here BΓ is the classifying space of the group Γ, and we denote by K−∞(R) the non-connective algebraic K-theory spectrum of the ring R. The homotopy groups of this spectrum are denoted Kn(R) and coincide with Quillen’s algebraic K-groups of R [Qui73] in positive dimensions and with the negative K-groups of Bass [Bas68] in negative dimensions. The homotopy groups of the spectrum X+∧K(R) are denot...
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We present the status of the Farrell-Jones Conjecture for algebraic K-theory for a group G and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be true and study inheritance properties. We discuss new applications, focussing on the Bass Conjecture, the Kaplansky Conjecture and conjectures generalizing Moody’s Induction Theorem. Thus we extend the class of gr...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-11150-x