Bianchi’s additional symmetries

In a 2012 note in Comptes Rendus Mathématique, the author did try to answer a question of Jean-Pierre Serre; it has recently been announced that the scope of that answer needs an adjustment, and the details of this adjustment are given in the present paper. The original question is the following. Co...

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Bibliographic Details
Published in:Journal of homotopy and related structures 2020-12, Vol.15 (3-4), p.455-462
Main Author: Rahm, Alexander D.
Format: Article
Language:English
Subjects:
Algebra
Algebraic Topology
Functional Analysis
Group Theory
Homology
K-Theory and Homology
Mathematics
Mathematics and Statistics
Number Theory
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Summary:In a 2012 note in Comptes Rendus Mathématique, the author did try to answer a question of Jean-Pierre Serre; it has recently been announced that the scope of that answer needs an adjustment, and the details of this adjustment are given in the present paper. The original question is the following. Consider the ring of integers  O in an imaginary quadratic number field, and the Borel–Serre compactification of the quotient of hyperbolic 3–space by SL 2 ( O ) . Consider the map  α induced on homology when attaching the boundary into the Borel–Serre compactification. How can one determine the kernel of   α (in degree 1) ? Serre used a global topological argument and obtained the rank of the kernel of  α . He added the question what submodule precisely this kernel is.
ISSN:2193-8407
1512-2891
DOI:10.1007/s40062-020-00262-4