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Geometriae Dedicata

, Volume 154, Issue 1, pp 93–101 | Cite as

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

  • Daniel Ruberman
  • Nikolai Saveliev
Original Paper

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.

Keywords

Dirac operator Seifert fibered homology sphere \({\bar\mu}\)-invariant η-invariant Seiberg–Witten equations 

Mathematics Subject Classification (2000)

57M27 57R57 11F20 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mathematics, MS 050Brandeis UniversityWalthamUSA
  2. 2.Department of MathematicsUniversity of MiamiCoral GablesUSA

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