Algebraic & Geometric Topology 12 (2012) 435–448

DOI: 10.2140/agt.2012.12.435

Abstract

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 = cl^ω(X), the connectivity weighted cone-length of X. We compute cl^ω(X) and kl^ω(X) for many spaces and give several examples.

Keywords

Lusternik–Schnirelmann category, categorical sequence, cone length, killing length, Egyptian fractions, mapping cone sequence

Mathematical Subject Classification

Primary: 55M30, 55P05

References

Publication

Received: 25 August 2011
Revised: 8 December 2011
Accepted: 8 December 2011
Published: 20 March 2012

Authors