Communications in Mathematical Physics

, Volume 142, Issue 1, pp 139–168 | Cite as

Adiabatic limits of the η-invariants the odd-dimensional Atiyah-Patodi-Singer problem

  • Ronald G. Douglas
  • Krzysztof P. Wojciechowski


We study the η-invariant of boundary value problems of Atiyah-Patodi-Singer type. We prove the formula for the spectral flow of the families overS1. Assuming a product structure in a collar neighbourhood of the boundary, we show that the η-invariant behaves the same way as on a closed manifold. We also study the “adiabatic” limit of the spectral invariants. In nice cases we are able to split them into a contribution from the interior, one from the cylinder, and an error term. Then we show that the error term disappears with the increasing length of the cylinder.


Neural Network Manifold Statistical Physic Complex System Error Term 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Ronald G. Douglas
    • 1
  • Krzysztof P. Wojciechowski
    • 2
  1. 1.Department of MathematicsSUNY at Stony BrookStony BrookUSA
  2. 2.Department of MathematicsIUPUIIndianapolisUSA

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