Existence of B^k_α,β-Structures on C^k-Manifolds

2019/08/12 by Yuri Ximenes Martins, Martins, Yuri Ximenes, Rodney Josué Biezuner +1
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1908.04442

openalex publication_date 2019/08/13 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce B_α,β^k-manifolds as generalizations of the notion of smooth manifolds with G-structure or with k-bounded geometry. These are C^k-manifolds whose transition functions φ_ji=φ_j∘φ_i^-1 are such that ∂^μφ_ji∈ B_α(r)∩ C^k-β(r) for every \vertμ\vert=r, where B=(B_r)_r∈Γ is some sequence of presheaves of Fréchet spaces endowed with further structures, Γ⊂ℤ_≥0 is some parameter set and α,β are functions. We present embedding theorems for the presheaf category of those structural presheaves B. The existence problem of B_α,β^k-structures on C^k-manifolds is studied and it is proved that under certain conditions on B, α and β, the forgetful functor from C^k-manifolds to B_α,β^k-manifolds has adjoints.

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