Translator Disclaimer
2006 Joins of DGA modules and sectional category
Lucía Fernández Suárez, Pierre Ghienne, Thomas Kahl, Lucile Vandembroucq
Algebr. Geom. Topol. 6(1): 119-144 (2006). DOI: 10.2140/agt.2006.6.119


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.


Download Citation

Lucía Fernández Suárez. Pierre Ghienne. Thomas Kahl. Lucile Vandembroucq. "Joins of DGA modules and sectional category." Algebr. Geom. Topol. 6 (1) 119 - 144, 2006.


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

zbMATH: 1097.55006
MathSciNet: MR2199456
Digital Object Identifier: 10.2140/agt.2006.6.119

Primary: 55M30
Secondary: 55P62

Rights: Copyright © 2006 Mathematical Sciences Publishers


Vol.6 • No. 1 • 2006
Back to Top