On the Homology stability range for symplectic groups
Marco Schlichting
TL;DR
This paper enhances the known homology stability ranges for symplectic groups over certain rings, establishing optimal bounds and linking obstructions to Milnor-Witt K-theory.
Contribution
It improves the stability range by a factor of 2 and connects the stability obstruction to Milnor-Witt K-theory, showing optimality in many cases.
Findings
Homology stability range doubled over previous results
Obstruction to further stability bounded by Milnor-Witt K-theory
Stability range is optimal in many cases
Abstract
We improve, by a factor of 2, known homology stability ranges for the integral homology of symplectic groups over commutative local rings with infinite residue field and show that the obstruction to further stability is bounded below by Milnor-Witt K-theory. In particular our stability range is optimal in many cases.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Geometric and Algebraic Topology