Space of real arc germs and Poincaré series of a semi-algebraic set (Q5928018)

The author investigates a real analogy of the theory developed by \textit{J. Denef} and \textit{F. Loeser} [Invent. Math. 135, 201-232 (1999; Zbl 0928.14004)]. First he defines arc spaces of germs of real arcs on semi-algebraic and real constructible sets. The geometry of these spaces yields new interesting invariants of semi-algebraic sets which are presented in the first section. Further on the author introduces a real version of the result of \textit{J. Pas} on the \(p\)-adic cell decomposition [J. Reine Angew. Math. 399, 137-172 (1989; Zbl 0666.12014)] in order to obtain a theorem on quantifier elimination. The author applies the technics developed in sections 2 and 3 to the study of the Poincaré series for a semi-algebraic set and to prove that such a series belongs in fact to \(\mathbb Q[T]\).