On Fico's Lemmata and the Homotopy Type of Certain Gyrations

2025/06/23 by Chenery, Sebastian
#57P10 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Primary 57N65 #Secondary 55P15

paper · doi:10.48550/arxiv.2506.18893

Abstract

We undertake to determine the homotopy type of gyrations of sphere products and of connected sums, thereby generalising results known in earlier literature as ''Fico's Lemmata'' which underpin gyrations in their original formulation from geometric topology. We provide applications arising from recasting these results into the modern homotopy theoretic setting.

Citations

• Stabilization of Poincaré duality complexes and homotopy gyrations
• Gyration Stability for Projective Planes
• Comparison techniques on inert top cell attachments
• Sphere fibrations over highly connected manifolds
• Homotopy of manifolds stabilized by projective spaces
• Circle actions and Suspension operations on Smooth manifolds
• Homotopy fibrations with a section after looping
• Intersections of Quadrics, Moment-angle Manifolds and Connected Sums

Related

• Stabilization of Poincaré duality complexes and homotopy gyrations
• Homotopy fibrations with a section after looping
• On h-Fibrations
• Gyration Stability for Projective Planes
• On spherical fibrations and Poincare complexes