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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.
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Contributor : Alexander Rahm <>
Submitted on : Tuesday, April 8, 2014 - 4:30:27 PM
Last modification on : Friday, March 19, 2021 - 10:04:01 PM
Long-term archiving on: : Tuesday, July 8, 2014 - 12:15:21 PM


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  • HAL Id : hal-00975454, version 1



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



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