2006/02/24 by Lucía Fernández Suárez, Lucia Fernandez Suarez, Pierre Ghienne +2 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Cohomology #Combinatorics #Computer science #Discrete mathematics #Fibration #Geometric and Algebraic Topology #Homotopy #Homotopy and Cohomology in Algebraic Topology #Joins #Kernel (algebra) #Mathematical analysis #Mathematics #Pure mathematics #Upper and lower bounds #math.AT #msc:55M30 #msc:55P62
paper · pdf · doi:10.2140/agt.2006.6.119
published as Algebr. Geom. Topol. 6 (2006) 119-144 · This is the version published by Algebraic & Geometric Topology on 24 February 2006
openalex publication_date 2006/02/24 · arxiv created 2009/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct an explicit semifree model for the fiber join of two fibrations pW E ! B and p 0 W E 0 ! B from semifree models of p and p 0 . 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 W H .BI / ! H .EI ./ In the special case of the evaluation fibration X I ! 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.