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

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2014


https://hal.archives-ouvertes.fr/hal-00975454
Contributeur : Alexander Rahm <>
Soumis le : mardi 8 avril 2014 - 16:30:27
Dernière modification le : mardi 8 avril 2014 - 16:33:38
Document(s) archivé(s) le : mardi 8 juillet 2014 - 12:15:21

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  • HAL Id : hal-00975454, version 1

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Rob De Jeu, Alexander Rahm. The image of the Borel-Serre bordification in algebraic K-theory. 2014. <hal-00975454>

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