The subgroup measuring the defect of the Abelianization of SL_2(Z[i])

Publication

The subgroup measuring the defect of the Abelianization of SL_2(Z[i])

Rahm, Alexander D.

Files

Defect__of_the_Abelianization_of_the_Picard_group.pdf

Adobe PDF, 117.39 KB

Identifiers

http://hdl.handle.net/10379/3783
https://doi.org/10.13025/15324

Publication Date

2013-02-10

Keywords

Picard modular group, Modular tree

Type

Article

Show all metadata

Citation

A.D.Rahm (2013) 'The subgroup measuring the defect of the Abelianization of SL_2(Z[i])'. Journal of Homotopy and Related Structures.

Abstract

There is a natural inclusion of SL2(Z) into SL2(Z[i]) , but it does not induce an injection of commutator factor groups (Abelianizations). In order to see where and how the 3 -torsion of the Abelianization of SL2(Z) disappears,we study a double cover of the amalgamated product decomposition SL2(Z)~=(Z/4Z)_(Z/2Z)(Z/6Z) inside SL2(Z[i]) ; and then compute the homology of the covering amalgam.

Funder

Publisher

Springer

Rights

Attribution-NonCommercial-NoDerivs 3.0 Ireland

Collections

Mathematics (Scholarly Articles)