Arc Spaces and Additive Invariants in Real Algebraic and Analytic Geometry
This book contains contributions prepared for a meeting in Aussois devoted to various properties and applications of analytic arcs on algebraic varieties. Two papers contain lecture notes of courses presented there. The contribution by M. Coste is devoted to topology of real algebraic sets. Algebraically constructible functions are the main tools used here giving rise to combinatorial topological invariants. The paper by K. Kurdyka and A. Parusiński introduces arc-symmetric sets and arc-analytic mappings. They are used to define a new topology that is stronger than Zariski topology. They show that Z2-homology classes of compact Nash manifolds can be represented by arc-symmetric semialgebraic sets. There are also two survey papers. The one written by C. McCrory and A. Parusiński describes algebraically constructible functions and conditions for a topological space to be homeomorphic to a real algebraic set. The paper by T. Fukui and L. Paunescu describes germs of maps, which can be transformed to real analytic ones by a locally finite number of blowing-ups.