A toral configuration space and regular semisimple conjugacy classes
1995 ◽
Vol 118
(1)
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pp. 105-113
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Keyword(s):
De Rham
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For any topological space X and integer n ≥ 1, denote by Cn(X) the configuration spaceThe symmetric group Sn acts by permuting coordinates on Cn(X) and we are concerned in this note with the induced graded representation of Sn on the cohomology space H*(Cn(X)) = ⊕iHi (Cn(X), ℂ), where Hi denotes (singular or de Rham) cohomology. When X = ℂ, Cn(X) is a K(π, 1) space, where π is the n-string pure braid group (cf. [3]). The corresponding representation of Sn in this case was determined in [5], using the fact that Cn(C) is a hyperplane complement and a presentation of its cohomology ring appears in [1] and in a more general setting, in [8] (see also [2]).
Keyword(s):
2020 ◽
Vol 29
(01)
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pp. 1950097
Keyword(s):
2017 ◽
Vol 26
(05)
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pp. 1750028
2007 ◽
Vol 04
(04)
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pp. 669-705
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2015 ◽
Vol 146
(1)
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pp. 79-105
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