The rational sectional category of certain maps

Abstract

We give a simple algebraic characterisation of the sectional category of rational maps admitting a homotopy retraction. As a particular case we get the Félix-Halperin theorem for rational Lusternik-Schnirelmann category and prove the conjecture of Jessup-Murillo-Parent on rational topological complexity. We also give a characterisation for relative category in the sense of Doeraene-El Haouari.

Final version. To appear in Ann. Scuola Norm-Sci

References in corpus (2)

• Joins of DGA modules and sectional category
• A Mapping Theorem for Topological Complexity

Cited by in corpus (3)

• Module sectional category of products
• The Ganea conjecture for rational approximations of sectional category
• Topological complexity of the work map