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 XI → 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.
Fernández Suárez, Lucía 1 ; Ghienne, Pierre 2 ; Kahl, Thomas 1 ; Vandembroucq, Lucile 1
@article{10_2140_agt_2006_6_119,
author = {Fern\'andez Su\'arez, Luc{\'\i}a and Ghienne, Pierre and Kahl, Thomas and Vandembroucq, Lucile},
title = {Joins of {DGA} modules and sectional category},
journal = {Algebraic and Geometric Topology},
pages = {119--144},
year = {2006},
volume = {6},
number = {1},
doi = {10.2140/agt.2006.6.119},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.119/}
}
TY - JOUR AU - Fernández Suárez, Lucía AU - Ghienne, Pierre AU - Kahl, Thomas AU - Vandembroucq, Lucile TI - Joins of DGA modules and sectional category JO - Algebraic and Geometric Topology PY - 2006 SP - 119 EP - 144 VL - 6 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.119/ DO - 10.2140/agt.2006.6.119 ID - 10_2140_agt_2006_6_119 ER -
%0 Journal Article %A Fernández Suárez, Lucía %A Ghienne, Pierre %A Kahl, Thomas %A Vandembroucq, Lucile %T Joins of DGA modules and sectional category %J Algebraic and Geometric Topology %D 2006 %P 119-144 %V 6 %N 1 %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.119/ %R 10.2140/agt.2006.6.119 %F 10_2140_agt_2006_6_119
Fernández Suárez, Lucía; Ghienne, Pierre; Kahl, Thomas; Vandembroucq, Lucile. Joins of DGA modules and sectional category. Algebraic and Geometric Topology, Tome 6 (2006) no. 1, pp. 119-144. doi: 10.2140/agt.2006.6.119
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