Joins of DGA modules and sectional category

Details Joins of DGA modules and sectional category Joins of DGA modules and sectional category

2009-02-27

arxiv.org/abs/0902.4823v1

Algebr. Geom. Topol. 6 (2006) 119-144

Mathematics

Algebraic Topology

This is the version published by Algebraic & Geometric Topology on 24 February 2006

Scientific paper

10.2140/agt.2006.6.119

We construct an explicit semifree model for the fiber join of two fibrations p: E --> B and p': E' --> B 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;Q) --> H^*(E;Q). In the special case of the evaluation fibration X^I --> X x 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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