• Corpus ID: 16250976

On Homological Stability for Configuration Spaces on Closed Background Manifolds

@article{Cantero2015OnHS,
  title={On Homological Stability for Configuration Spaces on Closed Background Manifolds},
  author={Federico Cantero and Martin Palmer},
  journal={arXiv: Algebraic Topology},
  year={2015}
}
We introduce a new map between configuration spaces of points in a background manifold - the replication map - and prove that it is a homology isomorphism in a range with certain coefficients. This is particularly of interest when the background manifold is closed, in which case the classical stabilisation map does not exist. We then establish conditions on the manifold and on the coefficients under which homological stability holds for configuration spaces on closed manifolds. These conditions… 

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