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arxiv: 2404.13776 · v1 · pith:PPEBPXTH · submitted 2024-04-21 · math.AT · math.KT· math.NT

Hopf algebras, Steinberg modules, and the unstable cohomology of SL_n(mathbb Z) and GL_n(mathbb Z)

Avner Ash , Jeremy Miller , Peter Patzt This is my paper

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classification math.AT math.KTmath.NT
keywords mathbbalgebracohomologycommutativegroupshopfsteinbergunstable
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We prove that the direct sum of all homology groups of the integral general linear groups with Steinberg module coefficients form a commutative Hopf algebra, in particular a free graded commutative algebra. We use this to construct new infinite families of unstable cohomology classes of $SL_n(\mathbb Z)$.

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