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ON THE SPLITTING PRINCIPLE FOR COHOMOLOGICAL INVARIANTS OF REFLECTION GROUPS

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Let k0 be a field of characteristic not two, (V, b) a finite-dimensional regular bilinear space over k0, and W a subgroup of the orthogonal group of (V, b) with the property that the subring of W-invariants of the symmetric algebra of V is a polynomial algebra over k0. We prove that Serre’s splitting principle holds for cohomological invariants of W with values in Rost’s cycle modules.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada

    STEFAN GILLE

  2. Bernoulli-Institute, University of Groningen, Nijenborgh 9, 9747, AG, Groningen, The Netherlands

    CHRISTIAN HIRSCH

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  1. STEFAN GILLE
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  2. CHRISTIAN HIRSCH
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Correspondence to STEFAN GILLE.

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Stefan Gille is supported by an NSERC grant.

Christian Hirsch is supported by The Danish Council for Independent Research–Natural Sciences, grant DFF–7014-00074 Statistics for point processes in space and beyond, and by the Centre for Stochastic Geometry and Advanced Bioimaging, funded by grant 8721 from the Villum Foundation.

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GILLE, S., HIRSCH, C. ON THE SPLITTING PRINCIPLE FOR COHOMOLOGICAL INVARIANTS OF REFLECTION GROUPS. Transformation Groups 27, 1261–1285 (2022). https://doi.org/10.1007/s00031-020-09637-6

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