Quasiconformal 4-manifolds

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