Spaces with Lusternik-Schnirelmann category n and cone length n + 1

Abstract

We construct a series of spaces, X(n), for each n > 0, such that cat(X(n)) = n and cl(X(n)) = n + 1. We show that the Hopf invariants determine whether the category of a space goes up when attaching a cell of top dimension. We give a new proof of counterexamples to a conjecture of Ganea. Also we introduce some techniques for manipulating cone decompositions. © 2000 Published by Elsevier Science Ltd. All rights reserved.