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Riemann-Roch-Grothendieck and torsion for foliations

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Abstract

In this article we prove a Riemann-Roch-Grothendieck theorem for the characteristic classes of a flat vector bundle over a foliation whose graph is Hausdorff. We assume that the strong foliation Novikov-Shubin invariants of the flat bundle are greater than three times the codimension of the foliation. Using transgression, we define a torsion form which in the odd acyclic case determines a Haefliger cohomology class which only depends on the foliation and the flat bundle. We construct examples where this torsion class is highly non-trivial.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street (m/c 249), 60607-7045, Chicago, Illinois

    James L. Heitsch & Connor Lazarov

  2. Department of Mathematics, Herbert Lehman College, CUNY, 10468, Bronx, New York

    James L. Heitsch & Connor Lazarov

Authors
  1. James L. Heitsch
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  2. Connor Lazarov
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Correspondence to James L. Heitsch.

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Heitsch, J.L., Lazarov, C. Riemann-Roch-Grothendieck and torsion for foliations. J Geom Anal 12, 437–468 (2002). https://doi.org/10.1007/BF02922049

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  • DOI: https://doi.org/10.1007/BF02922049

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