Functional Analysis and Its Applications

, Volume 52, Issue 2, pp 144–146 | Cite as

The Index of a 1-Form on a Real Quotient Singularity

  • S. M. Gusein-ZadeEmail author
  • W. Ebeling


Let G be a finite Abelian group acting (linearly) on space ℝn and, therefore, on its complexification ℂn, and let W be the real part of the quotient ℂn/G (in the general case, W ≠ ℝn/G). The index of an analytic 1-form on the space W is expressed in terms of the signature of the residue bilinear form on the G-invariant part of the quotient of the space of germs of n-forms on (ℝn, 0) by the subspace of forms divisible by the 1-form under consideration.

Key words

group action real quotient singularity 1-form index signature formula 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Institut für Algebraische GeometrieLeibnitz Universität HannoverHannoverGermany

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