Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes [unknown]

Jesús González, Mark Grant, Lucile Vandembroucq
2018 Contemporary Mathematics   unpublished
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 the
more » ... thors in their study of the sectional category of arbitrary maps. MSC 2010: 55M30, 55Q25, 55S35, 55S36, 68T40, 70B15.
doi:10.1090/conm/702/14109 fatcat:4rj6hg4tundapcua3rgxhqsdm4