JournalscmhVol. 84 , No. 2DOI 10.4171/cmh/163

Lower algebraic <var>K</var>-theory of hyperbolic 3-simplex reflection groups

  • Jean-François Lafont

    S.U.N.Y. Binghamton, USA
  • Ivonne J. Ortiz

    Miami University, Oxford, United States
Lower algebraic <var>K</var>-theory of hyperbolic 3-simplex reflection groups cover

Abstract

A hyperbolic 3-simplex reflection group is a Coxeter group arising as a lattice in O+(3,1), with fundamental domain a geodesic simplex in ℍ3 (possibly with some ideal vertices). The classification of these groups is known, and there are exactly 9 cocompact examples, and 23 non-cocompact examples. We provide a complete computation of the lower algebraic K-theory of the integral group ring of all the hyperbolic 3-simplex reflection groups.