A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is
Let X be a two-cell complex with attaching map α : S q → S p , and let C X be the cofiber of the diagonal inclusion X → X × X. It is shown that the topological complexity (TC ) of X agrees with the Lusternik-Schnirelmann category (cat ) of C X in the (almost stable) range q ≤ 2p − 1. In addition, the equality TC (X) = cat (C X ) is proved in the (strict) metastable range 2p − 1 < q ≤ 3(p − 1) under fairly mild conditions by making use of the Hopf invariant techniques recently developed by thedoi:10.1090/conm/702/14109 fatcat:4rj6hg4tundapcua3rgxhqsdm4