The period isomorphism in the tame geometry.

We describe singular homology of a manifold X$X$ via simplices σ:Δd→X$\sigma :\Delta _d\rightarrow X$ that satisfy Stokes' formula with respect to all differential forms. The notion is geared to the case of the 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 simplices. [ABSTRACT FROM AUTHOR]