Algebraic & Geometric Topology

Joins of DGA modules and sectional category

Lucía Fernández Suárez, Pierre Ghienne, Thomas Kahl, and Lucile Vandembroucq

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We construct an explicit semifree model for the fiber join of two fibrations p:EB and p:EB from semifree models of p and p. Using this model, we introduce a lower bound of the sectional category of a fibration p which can be calculated from any Sullivan model of p and which is closer to the sectional category of p than the classical cohomological lower bound given by the nilpotency of the kernel of p:H(B;)H(E;). In the special case of the evaluation fibration XIX×X we obtain a computable lower bound of Farber’s topological complexity TC(X). We show that the difference between this lower bound and the classical cohomological lower bound can be arbitrarily large.

Article information

Algebr. Geom. Topol., Volume 6, Number 1 (2006), 119-144.

Received: 1 November 2005
Revised: 11 January 2006
Accepted: 20 January 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space
Secondary: 55P62: Rational homotopy theory

Lusternik–Schnirelmann category sectional category topological complexity Sullivan models


Fernández Suárez, Lucía; Ghienne, Pierre; Kahl, Thomas; Vandembroucq, Lucile. Joins of DGA modules and sectional category. Algebr. Geom. Topol. 6 (2006), no. 1, 119--144. doi:10.2140/agt.2006.6.119.

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