Geodesic
On homological stability for configuration spaces on closed background manifolds
Documenta mathematica, Tome 20 (2015), pp. 753-805.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 are sharp when the background manifold is a two-dimensional sphere, the classical counterexample in the field. For field coefficients this extends results of Church citeChurch and Randal-Williams citeRW-hs-for-ucs to the case of odd characteristic, and for $p$-local coefficients it improves results of Bendersky--Miller citeBM.
Classification : 55R80, 55P60, 55R25
Keywords: homological stability, configuration spaces, replication map, scanning map, closed background manifolds 
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     author = {Cantero, Federico and Palmer, Martin},
     title = {On homological stability for configuration spaces on closed background manifolds},
     journal = {Documenta mathematica},
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     publisher = {mathdoc},
     volume = {20},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a19/}
}
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Cantero, Federico; Palmer, Martin. On homological stability for configuration spaces on closed background manifolds. Documenta mathematica, Tome 20 (2015), pp. 753-805. http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a19/