@article{22e148884ddf49eabd3504b95e35ac8e,
title = "Generating functions and topological complexity",
abstract = "We examine the rationality conjecture raised in [1] which states that (a) the formal power series ∑r≥1TCr+1(X)⋅xr represents a rational function of x with a single pole of order 2 at x=1 and (b) the leading coefficient of the pole equals cat(X). Here X is a finite CW-complex and for r≥2 the symbol TCr(X) denotes its r-th sequential topological complexity. We analyse an example (violating the Ganea conjecture) and conclude that part (b) of the rationality conjecture is false in general. Besides, we establish a cohomological version of the rationality conjecture.",
keywords = "Generating function, Lusternik - Schnirelmann category, Topological complexity",
author = "Michael Farber and Daisuke Kishimoto and Donald Stanley",
note = "Publisher Copyright: {\textcopyright} 2020",
year = "2020",
month = jun,
day = "1",
doi = "10.1016/j.topol.2020.107235",
language = "אנגלית",
volume = "278",
journal = "Topology and its Applications",
issn = "0166-8641",
publisher = "Elsevier B.V.",
}