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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

Abstract

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.

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

Information

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

Subjects:
Primary: 55M30
Secondary: 55P62

Rights: Copyright © 2006 Mathematical Sciences Publishers

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