The image of the Borel-Serre bordification in algebraic K-theory

Rob M. H. de Jeu (1) , Alexander D. Rahm (2)

1 Faculteit Exacte Wetenschappen Afdeling Wiskunde
2 NUIG - Department of Mathematics

We give a method for constructing explicit non-trivial elements in the third K-group (modulo torsion) of an imaginary quadratic number field. These arise from the relative homology of the map attaching the Borel-Serre boundary to the orbit space of the SL_2 group over the ring of imaginary quadratic integers on its symmetric space - hyperbolic three-space. We provide an algorithm which produces a chain of matrix quadruples specifying our element of K_3 of the field, modulo torsion. We carry out the algorithm for the Eisenteinian integers as well as for the imaginary quadratic integers of discriminant -7.

Domaines: K-théorie et homologie [math.KT]

Rob M. H. de Jeu, Alexander D. Rahm. The image of the Borel-Serre bordification in algebraic K-theory. 2014. ⟨hal-00975454⟩