Combinatorial Thom-Hirzebruch characteristic classes
Let \(M\) be the combinatorial manifold endowed with a flat combinatorial Riemannian metric. The family of measures \(\tau _t^d\) on \((d+1)\)-power of the manifold \(M\) is given by an integrable top degree differential form whose value at each point depends on the geometry on the \(t\)-neighborhood of the point. This construction produces a realization of the Thom-Hirzebruch measure \(\tau^d,\) introduced in [\textit{A. Connes, D. Sullivan}, and \textit{N. Teleman}, Topology 33, No. 4, 663-681 (1994; Zbl 0840.57013)]. One shows that when \(t\downarrow 0,\) \(\tau _t^d\) converge toward a simplicial chain representing the Thom-Hirzebruch homology class of corresponding degree.
scientific article; zbMATH DE number 1802385