Cohomology of 3-points configuration spaces of complex projective spaces

Ashraf, Samia; Berceanu, Barbu

doi:10.1515/advgeom-2014-0008

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Proofs Of Unstable and Stable Values1

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2016

2025

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Cited by 3 publications

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“…The stable Betti numbers of Conf n CP 2 prove Conjecture G of [42] which was first noticed by Kupers and Miller [28, Theorem 1.1] who computed the stable Betti numbers of Conf n CP 2 using McDuff's scanning map. Related computations are also done in [39,2].…”

Section: Proofs Of Unstable and Stable Valuesmentioning

confidence: 99%

Computing cohomology of configuration spaces

Maguire,

Christie,

Francour

2016

Preprint

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We give a concrete method to explicitly compute the rational cohomology of the unordered configuration spaces of connected, oriented, closed, even-dimensional manifolds of finite type which we have implemented in Sage [S + 09]. As an application, we give a complete computation of the stable and unstable rational cohomology of unordered configuration spaces in some cases, including that of CP 3 and a genus 1 Riemann surface, which is equivalently the homology of the elliptic braid group. In an appendix, we also give large tables of unstable and stable Betti numbers of unordered configuration spaces. From these, we empirically observe stability phenomenon in the unstable cohomology of unordered configuration spaces of some manifolds, some of which we prove and some of which we state as conjectures.

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Section: Proofs Of Unstable and Stable Valuesmentioning

confidence: 99%