The period isomorphism in tame geometry

2022/04/04 by Annette Huber, Huber, Annette · 1 citation
Computer Science · Mathematics · #03C64 #14P10 #58A10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Number Theory (math.NT) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2204.01402

openalex publication_date 2022/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe singular homology of a manifold X via simplices σ:Δ_d→ X that satisfy Stokes' formula with respect to all differential forms. The notion is geared to the case of tame geometry (definable manifolds with respect to an o-minimal structure), where it gives a description of the period pairing with de Rham cohomology via definable σ's.

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• On the de Rham theorem in the globally subanalytic setting

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