On the Homological Stability of Orthogonal and Spin Groups
Marco Schlichting, Sunny Sood
TL;DR
This paper advances the understanding of homological stability for orthogonal, special orthogonal, elementary orthogonal, and spin groups over certain local rings, extending previous stability ranges.
Contribution
It improves the homological stability ranges for these classical groups over local rings with infinite residue fields where 2 is invertible.
Findings
Extended stability ranges for orthogonal groups
Extended stability ranges for spin groups
Applicable to rings with infinite residue fields
Abstract
We improve homological stability ranges for the orthogonal group, special orthogonal group, elementary orthogonal group and the spin group over a commutative local ring with infinite residue field such that .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology