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Lower algebraic K-theory of certain reflection groups

Published online by Cambridge University Press:  20 November 2009

JEAN-FRANÇOIS LAFONT
Affiliation:
Department of Mathematics, Ohio State University, Columbus, OH 43210, U.S.A. e-mail: jlafont@math.ohio-state.edu
BRUCE A. MAGURN
Affiliation:
Department of Mathematics, Miami University, Oxford, OH 45056, U.S.A e-mail: magurnba@muohio.edu, ortizi@muohio.edu
IVONNE J. ORTIZ
Affiliation:
Department of Mathematics, Miami University, Oxford, OH 45056, U.S.A e-mail: magurnba@muohio.edu, ortizi@muohio.edu

Abstract

For P3 a finite volume geodesic polyhedron, with the property that all interior angles between incident faces are of the form π/mij (mij ≥ 2 an integer), there is a naturally associated Coxeter group ΓP. Furthermore, this Coxeter group is a lattice inside the semi-simple Lie group O+(3, 1) = Isom(3), with fundamental domain the original polyhedron P. In this paper, we provide a procedure for computing the lower algebraic K-theory of the integral group ring of such groups ΓP in terms of the geometry of the polyhedron P. As an ingredient in the computation, we explicitly calculate the K−1 and Wh of the groups Dn and Dn × 3, and we also summarize what is known about the 0.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2009

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