Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 6, Number 1 (2006), 119-144.
Joins of DGA modules and sectional category
We construct an explicit semifree model for the fiber join of two fibrations and from semifree models of and . Using this model, we introduce a lower bound of the sectional category of a fibration which can be calculated from any Sullivan model of and which is closer to the sectional category of than the classical cohomological lower bound given by the nilpotency of the kernel of . In the special case of the evaluation fibration we obtain a computable lower bound of Farber’s topological complexity . We show that the difference between this lower bound and the classical cohomological lower bound can be arbitrarily large.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space
Secondary: 55P62: Rational homotopy theory
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. https://projecteuclid.org/euclid.agt/1513796508