Local hyperbolicity, inert maps and Moore's conjecture

2025/04/14 by Ruizhi Huang, Huang, Ruizhi
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2504.09787

Abstract

We show that the base space of a homotopy cofibration is locally hyperbolic under various conditions. In particular, if these manifolds admit a rationally elliptic closure, then almost all punctured manifolds and almost all manifolds with rationally spherical boundary are ℤ/p^r-hyperbolic for almost all primes p and all integers r ≥ 1, and satisfy Moore's conjecture at sufficiently large primes.

Citations

• Comparison techniques on inert top cell attachments
• Top cell attachment for a Poincare Duality complex
• Homotopy of manifolds stabilized by projective spaces
• ℤ/p^r-hyperbolicity via homology
• p-hyperbolicity of homotopy groups via K-theory
• Homotopy fibrations with a section after looping
• Homotopy groups of highly connected Poincare duality complexes
• Exponential growth of homotopy groups of suspended finite complexes
• Moore's Conjecture for Polyhedral Products
• Homotopy groups of highly connected manifolds
• A combinatorial approach to the exponents of Moore spaces
• On the metastable homotopy of mod 2 Moore spaces
• Decomposition of loop spaces and periodic problem on π_*
• The Homotopy Type of a Poincaré Duality Complex after Looping
• Modular representations and the homotopy of low rank p-local CW-complexes
• On symmetric commutator subgroups, braids, links and homotopy groups
• Homotopy exponents for large H-spaces
• Free and semi-inert cell attachments
• Rational Homotopy Theory
• The Double Suspension and Exponents of the Homotopy Groups of Spheres

Related

• ℤ/p^r-hyperbolicity via homology
• On the Rational Hyperbolicity problem
• p-hyperbolicity of homotopy groups via K-theory
• Weakly Special Manifolds with no rational curves
• Infinitely many arithmetic hyperbolic rational homology 3-spheres that bound geometrically