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Boundaries, Eta Invariant and the Determinant Bundle

  • Richard Melrose
  • Frédéric Rochon
Part of the Trends in Mathematics book series (TM)

Abstract

Cobordism invariance shows that the index, in K-theory, of a family of pseudodifferential operators on the boundary of a fibration vanishes if the symbol family extends to be elliptic across the whole fibration. For Dirac operators with spectral boundary condition, Dai and Freed [5] gave an explicit version of this at the level of the determinant bundle. Their result, that the eta invariant of the interior family trivializes the determinant bundle of the boundary family, is extended here to the wider context of pseudodifferential families of cusp type.

Keywords

Eta invariant determinant line bundle 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Richard Melrose
    • 1
  • Frédéric Rochon
    • 2
  1. 1.Department of MathematicsMITCambridgeUSA
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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