Topological Complexity of H-Spaces
Algebraic Topology
2011-06-20 v1
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.
Cite
@article{arxiv.1106.3399,
title = {Topological Complexity of H-Spaces},
author = {Gregory Lupton and Jérôme Scherer},
journal= {arXiv preprint arXiv:1106.3399},
year = {2011}
}
Comments
11 pages