Generating functions and topological complexity

Michael Farber, Daisuke Kishimoto, Donald Stanley

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Publication statusPublished - Jun 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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