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arXiv · 1106.3399

Topological Complexity of H-Spaces

Gregory Lupton·Jérôme Scherer
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Abstract

Let X be a (not-necessarily homotopy-associative) H-space. We show that TC_{n+1}(X) = cat(X^n), for n >= 1, where TC_{n+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 TC_{n+1}(X), in the setting of a space Y acting on X.

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Gregory Lupton, Jérôme Scherer. 2011-06-17. Topological Complexity of H-Spaces. https://arxiv.org/abs/1106.3399

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