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A toral configuration space and regular semisimple conjugacy classes

Published online by Cambridge University Press:  24 October 2008

G. I. Lehrer
G. I. Lehrer
Affiliation:
School of Mathematics and Statistics, University of Sydney, Sydney, Australia2006
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Extract

For any topological space X and integer n ≥ 1, denote by Cn(X) the configuration space

The 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]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 1 , July 1995 , pp. 105 - 113
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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