Proceedings of The American Mathematical Society
Let X be a (not-necessarily homotopy-associative) H-space. We show that TCn+1(X) = cat (Xn), forn≥1, where TCn+1(−) denotes the so-called higher topological complexity introduced by Rudyak, and cat (−) denotes the Lusternik-Schnirelmann category. We also generalize this equality to an inequality, which gives an upper bound for TCn+1(X), in the setting of a space Y acting on X.
Lupton, Gregory and Scherer, Jerome, "Topological Complexity of H-Spaces" (2013). Mathematics Faculty Publications. 242.
First published in Proceedings of The American Mathematical Society in 2013, published by the American Mathematical Society.