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Abstract
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We consider certain descending filtrations of the ring of the
-
representation varieties of free groups and free abelian groups. By using them, we
introduce analogs of the Johnson homomorphisms of the automorphism groups of free
groups. We show that the first homomorphisms are extended to the automorphism
groups of free groups as crossed homomorphisms. Furthermore we show
that the extended crossed homomorphisms induce Kawazumi’s cocycles and
Morita’s cocycles. This is a generalization of our previous results for the
-representation
algebras.
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Keywords
$\mathrm{SL}(m,\mathbb{Q})$-representation varieties,
automorphism groups of free groups, Johnson homomorphisms
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Mathematical Subject Classification
Primary: 20F28
Secondary: 13A15, 20G05
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Milestones
Received: 23 April 2018
Revised: 23 December 2019
Accepted: 16 April 2021
Published: 31 August 2021
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