Equivariant, string and leading order characteristic classes associated to fibrations

Andrés Larraín-Hubach; Yoshiaki Maeda; Steven Rosenberg; Fabián Torres-Ardila

doi:10.1016/j.geomphys.2014.01.011

Equivariant, string and leading order characteristic classes associated to fibrations

Andrés Larraín-Hubach, Yoshiaki Maeda, Steven Rosenberg, Fabián Torres-Ardila

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

6 Citations (Scopus)

Abstract

Infinite rank vector bundles often appear as pushdowns of finite rank bundles from the total space of a fibration to the base space. The infinite rank bundles have string and leading order characteristic classes related to the characteristic classes of the finite rank bundles. We rewrite the ^S1-index theorem as a statement about equivariant leading order classes on loop spaces, interpret certain Gromov-Witten invariants in terms of leading order and string classes, show that the generators of the cohomology of a loop group are Chern-Simons string classes, and relate Donaldson invariants to leading order currents.

Original language	English
Pages (from-to)	34-52
Number of pages	19
Journal	Journal of Geometry and Physics
Volume	79
DOIs	https://doi.org/10.1016/j.geomphys.2014.01.011
Publication status	Published - 2014 May

Keywords

Characteristic classes
Donaldson classes
Equivariant index theorem
Gromov-Witten invariants
Infinite rank bundles
Loop group cohomology

ASJC Scopus subject areas

Mathematical Physics
Physics and Astronomy(all)
Geometry and Topology

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title = "Equivariant, string and leading order characteristic classes associated to fibrations",

abstract = "Infinite rank vector bundles often appear as pushdowns of finite rank bundles from the total space of a fibration to the base space. The infinite rank bundles have string and leading order characteristic classes related to the characteristic classes of the finite rank bundles. We rewrite the S1-index theorem as a statement about equivariant leading order classes on loop spaces, interpret certain Gromov-Witten invariants in terms of leading order and string classes, show that the generators of the cohomology of a loop group are Chern-Simons string classes, and relate Donaldson invariants to leading order currents.",

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year = "2014",

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AU - Larraín-Hubach, Andrés

AU - Maeda, Yoshiaki

AU - Rosenberg, Steven

AU - Torres-Ardila, Fabián

PY - 2014/5

Y1 - 2014/5

N2 - Infinite rank vector bundles often appear as pushdowns of finite rank bundles from the total space of a fibration to the base space. The infinite rank bundles have string and leading order characteristic classes related to the characteristic classes of the finite rank bundles. We rewrite the S1-index theorem as a statement about equivariant leading order classes on loop spaces, interpret certain Gromov-Witten invariants in terms of leading order and string classes, show that the generators of the cohomology of a loop group are Chern-Simons string classes, and relate Donaldson invariants to leading order currents.

AB - Infinite rank vector bundles often appear as pushdowns of finite rank bundles from the total space of a fibration to the base space. The infinite rank bundles have string and leading order characteristic classes related to the characteristic classes of the finite rank bundles. We rewrite the S1-index theorem as a statement about equivariant leading order classes on loop spaces, interpret certain Gromov-Witten invariants in terms of leading order and string classes, show that the generators of the cohomology of a loop group are Chern-Simons string classes, and relate Donaldson invariants to leading order currents.

KW - Characteristic classes

KW - Donaldson classes

KW - Equivariant index theorem

KW - Gromov-Witten invariants

KW - Infinite rank bundles

KW - Loop group cohomology

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