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

On universal modular symbols

Bruno Kahn (IMJ) , Fei Sun (IMJ) This is my paper

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classification math.KT math.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. The Goncharov Lie coalgebra of a field

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    Introduces Goncharov Lie coalgebra from GL homology and uses it with spectral sequences to describe rational K-theory of fields via weight-3 polylogarithms beyond prior low-degree cases.