Joins of DGA modules and sectional category

• Autor(a) principal: Fernández Suárez, Lucía
• Data de Publicação: 2006
• Outros Autores: Ghienne, Pierre, Kahl, Thomas, Vandembroucq, Lucile
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/11177
• topic: Lusternik–Schnirelmann category; Sectional category; Topological complexity; Sullivan models; Science & Technology

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.