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Infinitesimal index: cohomology computations

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Abstract

In this note we study the equivariant cohomology with compact supports of the zeroes of the moment map for the cotangent bundle of a linear representation of a torus and some of its notable subsets, using the theory of the infinitesimal index, developed in [8]. We show that, in analogy to the case of equivariant K-theory dealt with in [7] using the index of transversally elliptic operators, we obtain isomorphisms with notable spaces of splines studied in [2], [3].

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Authors and Affiliations

  1. Dip. Mat. Castelnuovo, Univ. di Roma La Sapienza, Rome, Italy

    C. De Concini & C. Procesi

  2. Centre de Mathématiques, Ecole Polytechnique, Palaiseau Cedex, F-91128, France

    M. Vergne

Authors
  1. C. De Concini
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  2. C. Procesi
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  3. M. Vergne
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Correspondence to C. De Concini.

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Dedicated to Tonny Springer

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De Concini, C., Procesi, C. & Vergne, M. Infinitesimal index: cohomology computations. Transformation Groups 16, 717–735 (2011). https://doi.org/10.1007/s00031-011-9144-7

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  • DOI: https://doi.org/10.1007/s00031-011-9144-7

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