A measure of the deviation from there being fibrations between a pair of compact manifolds

Abstract

In this paper we first study the topology of certain manifold complements. The obtained results are then used to show that the phi-category (cf. Lusternik-Schnirelmann category) of some pairs of manifolds is infinite. Finally, in the last section the equivariant case is considered, examples of equivariant mappings with infinitely many critical orbits being provided. (C) 2006 Elsevier B.V. All rights reserved.