2009/01/28 by J.M. García-Calcines, J. M. G. Calcines, Lucile Vandembroucq +1 · 1 citation
Mathematics · Medicine · Psychology · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Mathematics #Psychology #math.AT #msc:55M30
paper · pdf · doi:10.1112/jlms/jdq048
25 pages
arxiv created 2009/01/28 · openalex publication_date 2010/09/15 · arxiv updated 2014/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Based on a Whitehead-type characterization of the sectional category, we develop the notion of weak sectional category. This is a new lower bound of the sectional category, which is inspired by the notion of weak category in the sense of Berstein–Hilton. We establish several properties and inequalities, including the fact that the weak sectional category is a better lower bound for the sectional category than the classical one given by the nilpotency of the kernel of the induced map in cohomology. Finally, we apply our results in the study of the topological complexity in the sense of Farber.