The local equivalence problem in CR geometry

Martin Kolar

Department of Mathematical Analysis, Masaryk University, Janackovo nam. 2a, 602 00 Brno, Czech Republic


This article is dedicated to the centenary of the local CR equivalence problem, formulated by Henri Poincar\'{e} in 1907. The first part gives an account of Poincar\'{e}'s heuristic counting arguments, suggesting existence of infinitely many local CR invariants. Then we sketch the beautiful completion of Poincar\'{e}'s approach to the problem in the work of Chern and Moser on Levi nondegenerate hypersurfaces. The last part is an overview of recent progress in solving the problem on Levi degenerate manifolds.