Lusternik–Schnirelmann category and the connectivity ofX
Nicholas A. Scoville · Algebraic & Geometric Topology · 2012
We define and study a homotopy invariant called the connectivity weight to compute the weighted length between spaces X and Y .This is an invariant based on the connectivity of A i , where A i is a space attached in a mapping cone sequence from X to Y .We use the Lusternik-Schnirelmann category to prove a theorem concerning the connectivity of all spaces attached in any decomposition from X to Y .This theorem is used to prove that for any positive rational number q , there is a space X such that q D cl !.X /, the connectivity weighted cone-length of X .We compute cl !.X / and kl !.X / for many spaces and give several examples.