Linear stable range for homology of congruence subgroups via FI-modules
Wee Liang Gan, Liping Li
TL;DR
This paper establishes a linear bound on the homology of congruence subgroups of general linear groups using FI-modules, advancing understanding of their algebraic stability properties.
Contribution
It provides the first linear stable range result for the homology of congruence subgroups via a positive answer to a question about FI-modules.
Findings
Linear stable range for homology of congruence subgroups
Bound on presentation degree of FI-modules homology
Positive resolution of a key open question
Abstract
We answer positively a question of Church, Miller, Nagpal and Reinhold on existence of a linear bound on the presentation degree of the homology of a complex of FI-modules. This implies a linear stable range for the homology of congruence subgroups of general linear groups.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models