We define and study a homotopy invariant called the connectivity weight to compute the weighted length between spaces and . This is an invariant based on the connectivity of , where is a space attached in a mapping cone sequence from to . We use the Lusternik–Schnirelmann category to prove a theorem concerning the connectivity of all spaces attached in any decomposition from to . This theorem is used to prove that for any positive rational number , there is a space such that , the connectivity weighted cone-length of . We compute and for many spaces and give several examples.
"Lusternik–Schnirelmann category and the connectivity of $X$." Algebr. Geom. Topol. 12 (1) 435 - 448, 2012. https://doi.org/10.2140/agt.2012.12.435