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The \({\bar\mu}\)-invariant of Seifert fibered homology spheres and the Dirac operator

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Abstract

We derive a formula for the \({\bar\mu}\)-invariant of a Seifert fibered homology sphere in terms of the η-invariant of its Dirac operator. As a consequence, we obtain a vanishing result for the index of certain Dirac operators on plumbed 4-manifolds bounding such spheres.

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Authors and Affiliations

  1. Department of Mathematics, MS 050, Brandeis University, Waltham, MA, 02454, USA

    Daniel Ruberman

  2. Department of Mathematics, University of Miami, Coral Gables, FL, 33124, USA

    Nikolai Saveliev

Authors
  1. Daniel Ruberman
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  2. Nikolai Saveliev
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Correspondence to Nikolai Saveliev.

Additional information

The first author was partially supported by NSF Grant 0804760. The second author was partially supported by the Max-Planck-Institut für Mathematik in Bonn, Germany.

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Ruberman, D., Saveliev, N. The \({\bar\mu}\)-invariant of Seifert fibered homology spheres and the Dirac operator. Geom Dedicata 154, 93–101 (2011). https://doi.org/10.1007/s10711-010-9569-5

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  • DOI: https://doi.org/10.1007/s10711-010-9569-5

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