Quasiconformal 4-manifolds

1989/01/01 by Simon Donaldson, Dennis Sullivan · 3 citations
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Geometric Analysis and Curvature Flows #Mathematics #Pure mathematics #Mathematical analysis

paper · pdf · doi:10.1007/bf02392736

openalex publication_date 1989/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

For any pseudo-group of homeomorphism of Euclidean space one can define the corresponding category of manifolds. The most familiar examples in Topology are the full pseudo-group of homeomorphisms, giving rise to the theory of topological manifolds, and the subgroup of smooth differomorphisms giving rise to the theory of C ~ manifolds. In this paper, we discuss an intermediate category--quasiconformal homeomorphisms and manifolds. Recall that a homeomorphism 9 : D ~ R n from a domain D in R n to its image 9(D) is K quasiconformal if for all x in D

Citations

• An application of gauge theory to four-dimensional topology
• The orientation of Yang-Mills moduli spaces and 4-manifold topology
• Elliptic Partial Differential Equations of Second Order
• The Index of Elliptic Operators: I

Cited by

• Topological symplectic manifolds and bi-Lipschitz structures
• Boundary conformal field theories, limit sets of Kleinian groups and holography
• Atiyah–Singer index theorem [wikipedia]