Flat bundles on affine manifolds

Indranil Biswas; John Loftin; Matthias Stemmler

doi:10.1007/s40065-012-0064-8

Flat bundles on affine manifolds

Indranil Biswas, John Loftin, Matthias Stemmler

Rutgers Newark, Math & Computer Science

Research output: Contribution to journal › Review article › peer-review

6 Scopus citations

Abstract

We review some recent results in the theory of affine manifolds and bundles on them. Donaldson–Uhlenbeck–Yau type correspondences for flat vector bundles and principal bundles are shown. We also consider flat Higgs bundles and flat pairs on affine manifolds. A bijective correspondence between polystable flat Higgs bundles and solutions of the Yang–Mills–Higgs equation in the context of affine manifolds is shown. Also shown, in the context of affine manifolds, is a bijective correspondence between polystable flat pairs and solutions of the vortex equation. [Figure not available: see fulltext.]

Original language	English (US)
Pages (from-to)	159-175
Number of pages	17
Journal	Arabian Journal of Mathematics
Volume	2
Issue number	2
DOIs	https://doi.org/10.1007/s40065-012-0064-8
State	Published - Jun 1 2013

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1007/s40065-012-0064-8

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title = "Flat bundles on affine manifolds",

abstract = "We review some recent results in the theory of affine manifolds and bundles on them. Donaldson–Uhlenbeck–Yau type correspondences for flat vector bundles and principal bundles are shown. We also consider flat Higgs bundles and flat pairs on affine manifolds. A bijective correspondence between polystable flat Higgs bundles and solutions of the Yang–Mills–Higgs equation in the context of affine manifolds is shown. Also shown, in the context of affine manifolds, is a bijective correspondence between polystable flat pairs and solutions of the vortex equation. [Figure not available: see fulltext.]",

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T1 - Flat bundles on affine manifolds

AU - Biswas, Indranil

AU - Loftin, John

AU - Stemmler, Matthias

PY - 2013/6/1

Y1 - 2013/6/1

N2 - We review some recent results in the theory of affine manifolds and bundles on them. Donaldson–Uhlenbeck–Yau type correspondences for flat vector bundles and principal bundles are shown. We also consider flat Higgs bundles and flat pairs on affine manifolds. A bijective correspondence between polystable flat Higgs bundles and solutions of the Yang–Mills–Higgs equation in the context of affine manifolds is shown. Also shown, in the context of affine manifolds, is a bijective correspondence between polystable flat pairs and solutions of the vortex equation. [Figure not available: see fulltext.]

AB - We review some recent results in the theory of affine manifolds and bundles on them. Donaldson–Uhlenbeck–Yau type correspondences for flat vector bundles and principal bundles are shown. We also consider flat Higgs bundles and flat pairs on affine manifolds. A bijective correspondence between polystable flat Higgs bundles and solutions of the Yang–Mills–Higgs equation in the context of affine manifolds is shown. Also shown, in the context of affine manifolds, is a bijective correspondence between polystable flat pairs and solutions of the vortex equation. [Figure not available: see fulltext.]

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U2 - 10.1007/s40065-012-0064-8

DO - 10.1007/s40065-012-0064-8

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VL - 2

SP - 159

EP - 175

JO - Arabian Journal of Mathematics

JF - Arabian Journal of Mathematics

IS - 2

ER -

Flat bundles on affine manifolds

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