Extremal stability for configuration spaces
Ben Knudsen, Jeremy Miller, Philip Tosteson
TL;DR
This paper investigates the stability patterns in the high-dimensional rational homology of unordered configuration spaces of manifolds, using a novel approach related to Lie algebra homology.
Contribution
It introduces a general method to analyze stability phenomena in the homology of Lie algebras, applicable to configuration spaces.
Findings
Identifies stability patterns in high-dimensional homology
Develops a new approach based on Lie algebra homology
Provides insights potentially useful for broader topological studies
Abstract
We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenomena in the homology of Lie algebras, which may be of independent interest.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models