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

Abstract

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.