Lupton, Gregory
Scherer, Jerome
Topological Complexity Of H-Spaces
Proceedings Of The American Mathematical Society
0002-9939
141
5
1827-1838
12
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.
Lusternik-Schnirelmann category;
sectional category;
topological complexity;
H-space;
Amer Mathematical Soc
Providence
2013