An algebraic formula for the index of a 1-form on a real quotient singularity

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Authors

  • Wolfgang Ebeling
  • Sabir M. Gusein-Zade

Research Organisations

External Research Organisations

  • Lomonosov Moscow State University
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Details

Original languageEnglish
Pages (from-to)2543-2556
Number of pages14
JournalMathematische Nachrichten
Volume291
Issue number17-18
Early online date24 Jul 2018
Publication statusPublished - Dec 2018

Abstract

Let a finite abelian group G act (linearly) on the space ℝn and thus on its complexification ℂn. Let W be the real part of the quotient ℂn/G (in general W≠ℝn/G). We give an algebraic formula for the radial index of a 1-form on the real quotient W. It is shown that this index is equal to the signature of the restriction of the residue pairing to the G-invariant part ΩGω of Ωω=Ωnℝn,0/ω∧Ωn−1ℝn,0. For a G-invariant function f, one has the so-called quantum cohomology group defined in the quantum singularity theory (FJRW-theory). We show that, for a real function f, the signature of the residue pairing on the real part of the quantum cohomology group is equal to the orbifold index of the 1-form df on the preimage π−1(W) of W under the natural quotient map.

Keywords

    1-form, group action, index, real quotient singularity, signature formula

ASJC Scopus subject areas

Cite this

An algebraic formula for the index of a 1-form on a real quotient singularity. / Ebeling, Wolfgang; Gusein-Zade, Sabir M.
In: Mathematische Nachrichten, Vol. 291, No. 17-18, 12.2018, p. 2543-2556.

Research output: Contribution to journal › Article › Research › peer review

Ebeling W, Gusein-Zade SM. An algebraic formula for the index of a 1-form on a real quotient singularity. Mathematische Nachrichten. 2018 Dec;291(17-18):2543-2556. Epub 2018 Jul 24. doi: 10.48550/arXiv.1708.09219, 10.1002/mana.201700453
Ebeling, Wolfgang ; Gusein-Zade, Sabir M. / An algebraic formula for the index of a 1-form on a real quotient singularity. In: Mathematische Nachrichten. 2018 ; Vol. 291, No. 17-18. pp. 2543-2556.
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