## Topological Complexity Of H-Spaces

Let X be a (not-necessarily homotopy-associative) H-space. We show that TCn+1(X) = cat(X-n), for n >= 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.

Published in:
Proceedings Of The American Mathematical Society, 141, 5, 1827-1838
Year:
2013
Publisher:
Providence, Amer Mathematical Soc
ISSN:
0002-9939
Keywords:
Laboratories: