Equivariant indices of vector fields and 1-forms

Wolfgang Ebeling; Sabir M. Gusein-Zade

doi:10.1007/s40879-015-0036-6

Equivariant indices of vector fields and 1-forms

Wolfgang Ebeling^*
, Sabir M. Gusein-Zade

^*Corresponding author for this work

Institute of Algebraic Geometry

Lomonosov Moscow State University

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

Abstract

Equivariant versions of the radial index and of the GSV-index of a vector field or a 1-form on a singular variety with an action of a finite group are defined. They have values in the Burnside ring of the group. Poincaré–Hopf type theorems for them are proven and some of their properties are described.

Original language	English
Pages (from-to)	286-301
Number of pages	16
Journal	European Journal of Mathematics
Volume	1
Issue number	2
DOIs	https://doi.org/10.1007/s40879-015-0036-6
Publication status	Published - 1 Jun 2015

Keywords

1-Forms
Burnside ring
Finite group action
Index
Singularities
Vector fields

ASJC Scopus subject areas

General Mathematics

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10.1007/s40879-015-0036-6

Cite this

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title = "Equivariant indices of vector fields and 1-forms",

abstract = "Equivariant versions of the radial index and of the GSV-index of a vector field or a 1-form on a singular variety with an action of a finite group are defined. They have values in the Burnside ring of the group. Poincar{\'e}–Hopf type theorems for them are proven and some of their properties are described.",

keywords = "1-Forms, Burnside ring, Finite group action, Index, Singularities, Vector fields",

author = "Wolfgang Ebeling and Gusein-Zade, \{Sabir M.\}",

note = "Funding information: Partially supported by the DFG (Mercator fellowship, Eb 102/8–1), the Russian government grant 11.G34.31.0005, RFBR–13-01-00755, and NSh–4850.2012.1.",

year = "2015",

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doi = "10.1007/s40879-015-0036-6",

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journal = "European Journal of Mathematics",

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T1 - Equivariant indices of vector fields and 1-forms

AU - Ebeling, Wolfgang

AU - Gusein-Zade, Sabir M.

N1 - Funding information: Partially supported by the DFG (Mercator fellowship, Eb 102/8–1), the Russian government grant 11.G34.31.0005, RFBR–13-01-00755, and NSh–4850.2012.1.

PY - 2015/6/1

Y1 - 2015/6/1

N2 - Equivariant versions of the radial index and of the GSV-index of a vector field or a 1-form on a singular variety with an action of a finite group are defined. They have values in the Burnside ring of the group. Poincaré–Hopf type theorems for them are proven and some of their properties are described.

AB - Equivariant versions of the radial index and of the GSV-index of a vector field or a 1-form on a singular variety with an action of a finite group are defined. They have values in the Burnside ring of the group. Poincaré–Hopf type theorems for them are proven and some of their properties are described.

KW - 1-Forms

KW - Burnside ring

KW - Finite group action

KW - Index

KW - Singularities

KW - Vector fields

UR - https://www.scopus.com/pages/publications/84958691176

UR - https://arxiv.org/abs/1307.2054

U2 - 10.1007/s40879-015-0036-6

DO - 10.1007/s40879-015-0036-6

M3 - Article

AN - SCOPUS:84958691176

SN - 2199-675X

VL - 1

SP - 286

EP - 301

JO - European Journal of Mathematics

JF - European Journal of Mathematics

IS - 2

ER -

Equivariant indices of vector fields and 1-forms

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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