TY - JOUR

T1 - The Index of a 1-Form on a Real Quotient Singularity

AU - Ebeling, Wolfgang

AU - Gusein-Zade, Sabir M.

N1 - Funding information: ?The work of the first author (the formulation of the problem and the development of the ingredients of the proof related to the residue pairing) was supported by Russian Science Foundation grant 16-11-10018. The work of the second author was partially supported by DFG.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - 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.

AB - 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.

KW - 1-form

KW - group action

KW - index

KW - real quotient singularity

KW - signature formula

UR - http://www.scopus.com/inward/record.url?scp=85049599406&partnerID=8YFLogxK

U2 - 10.1007/s10688-018-0220-9

DO - 10.1007/s10688-018-0220-9

M3 - Article

AN - SCOPUS:85049599406

VL - 52

SP - 144

EP - 146

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 2

ER -