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A geometric criterion for the boundedness of characteristic classes

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Abstract

We show that for a connected Lie group G, the linearity of its radical \({\sqrt G}\) (that is of its biggest connected normal solvable subgroup), is a necessary and sufficient condition for the boundedness of all Borel cohomology classes of G with integer coefficients, and that the linearity of \({\sqrt G}\) is also equivalent to a large-scale geometric property of G (involving distortion).

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Author information

Authors and Affiliations

  1. MAPMO Université d’Orléans, Orléans, France

    Indira Chatterji

  2. Department of Mathematics, ETHZ, Zürich, Switzerland

    Guido Mislin

  3. CMI Université d’Aix-Marseille I, Marseille, France

    Christophe Pittet

  4. Department of Mathematics, Cornell University, New York, USA

    Laurent Saloff-Coste

Authors
  1. Indira Chatterji
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  2. Guido Mislin
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  3. Christophe Pittet
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  4. Laurent Saloff-Coste
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Corresponding author

Correspondence to Christophe Pittet.

Additional information

I. Chatterji is partially supported by the NSF grant No. 0644613 and the ANR grant JC-318197 QuantiT.

C. Pittet is partially supported by the CNRS, déc. no 080026DRH. L. Saloff-Coste is partially supported by NSF grants DMS-0603886 and DMS-1004771.

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Chatterji, I., Mislin, G., Pittet, C. et al. A geometric criterion for the boundedness of characteristic classes. Math. Ann. 351, 541–569 (2011). https://doi.org/10.1007/s00208-010-0610-7

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  • DOI: https://doi.org/10.1007/s00208-010-0610-7

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