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Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes
[unknown]
2018
Contemporary Mathematics
unpublished
Preserved Fulltext
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
doi:10.1090/conm/702/14109
fatcat:4rj6hg4tundapcua3rgxhqsdm4