Geodesic
The Index of a 1-Form on a Real Quotient Singularity
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 78-81

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Let $G$ be a finite Abelian group acting (linearly) on space $\mathbb{R}^n$ and, therefore, on its complexification $\mathbb{C}^n$, and let $W$ be the real part of the quotient $\mathbb{C}^n/G$ (in the general case, $W \neq\mathbb{R}^n/G$). 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 $(\mathbb{R}^n,0)$ by the subspace of forms divisible by the 1-form under consideration.
Mots-clés : group action, 1-form, signature formula.
Keywords: real quotient singularity, index 
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     author = {S. M. Gusein-Zade and W. Ebeling},
     title = {The {Index} of a {1-Form} on a {Real} {Quotient} {Singularity}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {2018},
     language = {ru},
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S. M. Gusein-Zade; W. Ebeling. The Index of a 1-Form on a Real Quotient Singularity. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 78-81. http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a6/