Linear representations of Aut(Fr) on the homology of representation varieties

Let G be a compact semisimple linear Lie group. We study the action of Aut ( F r ) on the space H ∗ ( G r ; Q ) . We compute the image of this representation and prove that it only depends on the rank of g . We show that the kernel of this representation is always the Torrelli subgroup IA r of Aut (...

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Bibliographic Details
Published in:Geometriae dedicata 2020-12, Vol.209 (1), p.199-206
Main Authors: Algom-Kfir, Yael, Hadari, Asaf
Format: Article
Language:English
Subjects:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Homology
Hyperbolic Geometry
Lie groups
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Representations
Subgroups
Topology
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Summary:Let G be a compact semisimple linear Lie group. We study the action of Aut ( F r ) on the space H ∗ ( G r ; Q ) . We compute the image of this representation and prove that it only depends on the rank of g . We show that the kernel of this representation is always the Torrelli subgroup IA r of Aut ( F r ) .
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-020-00530-w