The Index of a 1-Form on a Real Quotient Singularity
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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 wordsgroup action real quotient singularity 1-form index signature formula
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- G. N. Khimshiashvili, Comm. Acad. Sci. Georgian SSR [in Russian], 85:2 (1977), 309–311.Google Scholar