TY - JOUR

T1 - Generating functions and topological complexity

AU - Farber, Michael

AU - Kishimoto, Daisuke

AU - Stanley, Donald

N1 - Funding Information:
M. Farber was partially supported by a grant from the Leverhulme Foundation.
Publisher Copyright:
© 2020

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.topol.2020.107235

DO - 10.1016/j.topol.2020.107235

M3 - Article

AN - SCOPUS:85083806172

VL - 278

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

M1 - 107235

ER -