Indices of collections of equivariant 1-forms and characteristic numbers

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autorschaft

  • Wolfgang Ebeling
  • Sabir M. Gusein-Zade

Organisationseinheiten

Externe Organisationen

  • Lomonosov Moscow State University
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Details

OriginalspracheEnglisch
Seiten (von - bis)153-162
Seitenumfang10
FachzeitschriftTopology and its applications
Jahrgang191
PublikationsstatusVeröffentlicht - 5 Aug. 2015

Abstract

If two closed G-manifolds are G-cobordant then characteristic numbers corresponding to the fixed point sets (submanifolds) of subgroups of G and to normal bundles to these sets coincide. We construct two analogues of these characteristic numbers for singular complex G-varieties where G is a finite group. They are defined as sums of certain indices of collections of 1-forms (with values in the spaces of the irreducible representations of subgroups). These indices are generalizations of the GSV-index (for isolated complete intersection singularities) and the Euler obstruction respectively.

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Indices of collections of equivariant 1-forms and characteristic numbers. / Ebeling, Wolfgang; Gusein-Zade, Sabir M.
in: Topology and its applications, Jahrgang 191, 05.08.2015, S. 153-162.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Ebeling W, Gusein-Zade SM. Indices of collections of equivariant 1-forms and characteristic numbers. Topology and its applications. 2015 Aug 5;191:153-162. doi: 10.1016/j.topol.2015.06.002
Ebeling, Wolfgang ; Gusein-Zade, Sabir M. / Indices of collections of equivariant 1-forms and characteristic numbers. in: Topology and its applications. 2015 ; Jahrgang 191. S. 153-162.
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T1 - Indices of collections of equivariant 1-forms and characteristic numbers

AU - Ebeling, Wolfgang

AU - Gusein-Zade, Sabir M.

N1 - Funding information: Partially supported by DFG (Mercator fellowship, Eb 102/8–1 ), RFBR–13-01-00755 , and NSh–5138.2014.1 .

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AB - If two closed G-manifolds are G-cobordant then characteristic numbers corresponding to the fixed point sets (submanifolds) of subgroups of G and to normal bundles to these sets coincide. We construct two analogues of these characteristic numbers for singular complex G-varieties where G is a finite group. They are defined as sums of certain indices of collections of 1-forms (with values in the spaces of the irreducible representations of subgroups). These indices are generalizations of the GSV-index (for isolated complete intersection singularities) and the Euler obstruction respectively.

KW - Characteristic numbers

KW - Equivariant 1-forms

KW - Finite group action

KW - Indices

KW - Singularities

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UR - https://arxiv.org/abs/1406.4278

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