Topological invariance of the combinatorial Euler characteristic of tame spaces (Q643525)

The combinatorial Euler characteristic for tame spaces can be defined by tame triangulations and a formula similar to the classical one. The author proves that the combinatorial Euler characteristic is a homeomorphism invariant. The result is related to Milnor's disproof of the polyhedral Hauptvermutung and the apparent lack of cohomological interpretation of the combinatorial Euler characteristic of tame spaces that are not locally compact. The result is proved in the setting of o-minimal structures over \(\mathbb{R}\). The author uses the canonical, topologically defined stratification of tame spaces by locally compact, tame strata.