Higher homotopy normalities in topological groups

Abstract

AbstractThe purpose of this paper is to introduce ‐maps (), which describe higher homotopy normalities, and to study their basic properties and examples. An ‐map is defined with higher homotopical conditions. It is shown that a homomorphism is an ‐map if and only if there exists fiberwise maps between fiberwise projective spaces with some properties. Also, the homotopy quotient of an ‐map is shown to be an ‐space if its LS category is not greater than . As an application, we investigate when the inclusions and are ‐locally ‐maps.