Self-dual connections and the topology of smooth 4-manifolds

DOI10.1090/S0273-0979-1983-15090-5zbMath0519.57012WikidataQ54250741 ScholiaQ54250741MaRDI QIDQ3668501

Simon K. Donaldson

Publication date: 1983

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

singularitiesmoduli spaceself-dual connectionsYang-Mills theorygauge theoryKummer surfaceoriented cobordismexotic differentiable structures on 4-spacefailure of smooth surgery in four dimensionsfirst Stiefel-Whitney class for the analytic index of family of elliptic differential operatorsgauge equivalence classes of smooth connectionsintersection form of a smooth, compact, simply connected oriented four- dimensional manifold

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Constructive quantum field theory (81T08) Characteristic classes and numbers in differential topology (57R20) Index theory and related fixed-point theorems on manifolds (58J20) Applications of global differential geometry to the sciences (53C80) Differentiable structures in differential topology (57R55) Connections (general theory) (53C05) Algebraic topology on manifolds and differential topology (57R19)

Related Items

Fields of 2-planes on compact simply-connected smooth 4-manifolds, The impact of Thom’s cobordism theory, Topology through the centuries: Low dimensional manifolds, Homology cobordism, knot concordance, and Heegaard Floer homology, Morse theory interpretation of topological quantum field theories, Instantons on Calabi-Yau and hyper-Kähler cones, Yang-Mills replacement, Unnamed Item, Representing homology classes of almost definite 4-manifolds, Independence of iterated Whitehead doubles, Higher-order intersections in low-dimensional topology, A comparison of solution generating techniques for the self-dual Yang–Mills equations, Shake-slice knots and smooth contractible 4-manifolds, The geometry of gauge fields, Topological concordance and F-isotopy, Numerical Minimization of Dirichlet Laplacian Eigenvalues of Four-Dimensional Geometries, Instantons on Calabi-Yau cones

Cites Work

• Self-dual Yang-Mills connections on non-self-dual 4-manifolds
• Self-duality in four-dimensional Riemannian geometry
• An Infinite Dimensional Version of Sard's Theorem
• Removable singularities in Yang-Mills fields
• Unnamed Item
• Unnamed Item