The based \(\text{SU}(n)\)-instanton moduli spaces
type: Item
instance of: scholarly article
title: The based \(\text{SU}(n)\)-instanton moduli spaces
zbMATH Open document ID: 0788.32013
DOI: 10.1007/BF01459729
author: Youliang Tian
published in: Mathematische Annalen
publication date: 1994-05-26T00:00:00Z
full work available at URL: https://eudml.org/doc/165165
review text: We give an \(L\)-stratification of \({\mathcal M}_ k\), the based moduli space of \(SU(n)\) instantons of charge \(k\) over \(S^ 4\). Then we prove that the stabilization map \(\iota_ k:{\mathcal M}_ k \to {\mathcal M}_{k+1}\) is an equivalence through a range \(q(k)\) which monotonically increases and tends to infinite as \(k \to \infty\). This proves the Atiyah-Jones conjecture for the group \(SU(n)\). As a by-product of the \(L\)- stratification we are able to conclude that \({\mathcal M}_ k\) are simply connected for all \(k\) and all \(n>2\).
Mathematics Subject Classification ID: 32G13
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 55P35
zbMATH DE Number: 537311
zbMATH Keywords: \(SU(n)\) instantons
zbMATH Keywords: moduli space
reviewed by: Yichao Tian
MaRDI profile type: Publication
cites work: Instantons in two and four dimensions
cites work: Construction of instantons
cites work: Self-duality in four-dimensional Riemannian geometry
cites work: Topological aspects of Yang-Mills theory
cites work: The topology of instanton moduli spaces. I: The Atiyah-Jones conjecture
cites work: The topology of the space of rational maps into generalized flag manifolds
cites work: On the Homology of SU(n) Instantons
cites work: Homology operations on instantons
cites work: Full holomorphic maps from the Riemann sphere to complex projective spaces
cites work: Q3998602
cites work: Instantons and geometric invariant theory
cites work: On the topology of spaces of holomorphic maps
cites work: Q4143433
cites work: Instantons and jumping lines
cites work: Some spaces of holomorphic maps to complex Grassmann manifolds
cites work: On the moduli space of \(SU(n)\) monopoles and holomorphic maps to flag manifolds
cites work: The stable topology of self-dual moduli spaces
description: scientific article; zbMATH DE number 537311