Objective B-Fields and a Hitchin-Kobayashi Correspondence
Shuguang Wang
TL;DR
This paper introduces objective B-fields to refine characteristic classes of twisted bundles, defines objective stability and Einstein metrics, and establishes a new Hitchin-Kobayashi correspondence, proving the orientability of the SO(3)-instanton moduli space.
Contribution
It presents a novel approach using objective B-fields to refine characteristic classes and establishes a new Hitchin-Kobayashi correspondence for twisted bundles.
Findings
Objective B-fields refine characteristic classes.
A new Hitchin-Kobayashi correspondence is established.
The SO(3)-instanton moduli space is proven to be orientable.
Abstract
A simple trick invoking objective B-fields is employed to refine the concept of characteristic classes for twisted bundles. Then the objective stability and objective Einstein metrics are introduced and a new Hitchin-Kobayashi correspondence is established between them. As an application the SO(3)-instanton moduli space is proved to be always orientable.
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Taxonomy
TopicsGeometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology · Advanced Differential Geometry Research