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The period map and the intersection form

  • V. I. Arnold
  • S. M. Gusein-Zade
  • A. N. Varchenko
Chapter
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

Let us be given a smooth fibration and a differential form on the space of fibration which is closed on the fibres. In such a situation there arises the period map of the form – a many-valued map from the base of the fibration to the cohomology of the fibre. A point of the base is mapped to the cohomology class of the form in the fibre over the point translated to the cohomology of a distinguished fibre. The fact that it is many-valued arises from the fact that there is not a unique choice of path for the translation.

Keywords

Intersection Form Cohomology Class Symplectic Structure Cotangent Bundle Holomorphic Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • V. I. Arnold
  • S. M. Gusein-Zade
    • 1
  • A. N. Varchenko
    • 2
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of MathematicsThe University of North Carolina at Chapel HillChapel HillUSA

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