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Bounded characteristic classes and flat bundles

Abstract : Let G be a connected Lie group, G^d the underlying discrete group, and BG, BG^d their classifying spaces. Let R denote the radical of G. We show that all classes in the image of the canonical map in cohomology H^*(BG,R)->H^*(BG^d,R) are bounded if and only if the derived group [R,R] is simply connected. We also give equivalent conditions in terms of stable commutator length and distortion.
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https://hal.archives-ouvertes.fr/hal-01145333
Contributor : Indira Chatterji <>
Submitted on : Thursday, April 23, 2015 - 8:09:30 PM
Last modification on : Thursday, January 23, 2020 - 6:22:16 PM

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  • HAL Id : hal-01145333, version 1
  • ARXIV : 1202.4069

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Indira Chatterji, Yves de Cornulier, Guido Mislin, Christophe Pittet. Bounded characteristic classes and flat bundles. Journal of Differential Geometry, 2013, 95 (1), pp.39 - 51. ⟨hal-01145333⟩

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