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On universal modular symbols

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arxiv 1407.0475 v2 pith:NQ5ISI53 submitted 2014-07-02 math.KT math.NT

Bruno Kahn (IMJ) , Fei Sun (IMJ) This is my paper · ORCID
classification math.KTmath.NT
keywords homologylinearrelationshipash-rudolphbuildingcaseclarifycoefficients
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We clarify the relationship between works of Lee-Szczarba and Ash-Rudolph on the homology of the Steinberg module of a linear Tits building. This yields a simple proof of the Solomon-Tits theorem in this special case. We also give a (weak) relationship between this combinatorics and the one studied by van der Kallen, Suslin and Nesterenko to compute the homology of the general linear group with constant coefficients.

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  1. Presenting restricted Steinberg modules of general linear groups

    math.RT 2026-07 accept novelty 6.0 of 10

    Restricted Steinberg modules of GL_n admit unimodular apartment generators and Bykovskii/circuit presentations, and their coinvariants compute relative homology of partial Borel–Serre compactifications.

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