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

2016/07/29 by González, Jesús, Grant, Mark, Vandembroucq, Lucile
#55M30 #55Q25 #55S35 #55S36 #68T40 #70B15 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.08858

Abstract

Let X be a two-cell complex with attaching map α\colon 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 (\rm TC) of X agrees with the Lusternik-Schnirelmann category (\rm cat) of C_X in the (almost stable) range q≤2p-1. In addition, the equality \rm TC(X)=\rm cat(C_X) is proved in the (strict) metastable range 2p-1

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