Joins of DGA modules and sectional category
Abstract
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.
Cite
@article{arxiv.0902.4823,
title = {Joins of DGA modules and sectional category},
author = {Lucia Fernandez Suarez and Pierre Ghienne and Thomas Kahl and Lucile Vandembroucq},
journal= {arXiv preprint arXiv:0902.4823},
year = {2009}
}
Comments
This is the version published by Algebraic & Geometric Topology on 24 February 2006