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manuscripta mathematica

, Volume 95, Issue 1, pp 189–212 | Cite as

Theη-form and a generalized maslov index

  • U. Bunke
  • H. Koch
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Abstract

Given a family {L 0(b,L 1(b)} bB of pairs of transverse Lagrangian subspaces of a hermitean symplectic vector space we define a family of Dirac operators on the unit interval and consider itsη-formη(L 0,L 1) εΘ*(B). To a family {L 0(b,L 1(b,L 2(b)} bB of pairwise transverse Lagrangian subspaces we associate the cocycleη(L 0,L 1)+η(L 1,L 2)+η(L 2,L 1) which is a closed form. We identify its cohomology class with a generalization to families of the triple Maslov index.

Mathematics Subject Classification (1991)

58G10 58G20 

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • U. Bunke
    • 1
    • 2
  • H. Koch
    • 1
    • 2
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenGermany
  2. 2.Institut für Angewandte MathematikUniversität HeidelbergHeidelbergGermany

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