Generating functions and topological complexity

Michael Farber*, Daisuke Kishimoto, Donald Stanley

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number107235
JournalTopology and its Applications
Volume278
DOIs
StatePublished - 1 Jun 2020
Externally publishedYes

Keywords

  • Generating function
  • Lusternik - Schnirelmann category
  • Topological complexity

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