Secondary cohomology operations and sectional category

2025/12/22 by Mark D Grant, Grant, Mark
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory

paper · doi:10.48550/arxiv.2512.19461

Abstract

We show how secondary cohomology operations in the total space of the fibred join can be used to give lower bounds for the sectional category of a fibration. This suggests a refinement of the module weight of Iwase--Kono, which we call the secondary module weight. Examples are given for which the secondary module weight at the prime 2 detects sectional category while the module weight does not.

Citations

• Rational approximations of sectional category and Poincaré duality
• Hopf Invariants for sectional category with applications to topological\n robotics
• The module category weight of compact exceptional Lie groups
• On higher analogs of topological complexity
• Robot motion planning, weights of cohomology classes, and cohomology operations
• Lusternik-Schnirelmann category of Spin9
• The sectional category of a map
• Instabilities of Robot Motion
• Topological complexity of motion planning

Related

• Sectional number of a morphism
• Computations in rational sectional category
• Sectional Category and the parametrized Borsuk-Ulam property
• Upper and lower bounds of the (co)chain type level of a space
• Relative sectional category revisited