# LOCALIZATION AND HOMOLOGICAL STABILITY OF CONFIGURATION SPACES

@article{Bendersky2012LOCALIZATIONAH, title={LOCALIZATION AND HOMOLOGICAL STABILITY OF CONFIGURATION SPACES}, author={Martin Bendersky and Jeremy B. Miller}, journal={Quarterly Journal of Mathematics}, year={2012}, volume={65}, pages={807-815} }

In [Chu12], Church used representation stability to prove that the space of configurations of distinct unordered points in a closed manifold exhibit rational homological stability. A second proof was also given by Randal-Williams in [RW11] using transfer maps. We give a third proof of this fact using localization and rational homotopy theory. This gives new insight into the role that the rationals play in homological stability. Our methods also yield new information about stability for torsion… CONTINUE READING

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## Coincidences between homological densities, predicted by arithmetic

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## On Homological Stability for Configuration Spaces on Closed Background Manifolds

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## Homology Stability for Spaces of Surfaces

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