1959/05/01 by Aldo Andreotti, Theodore Frankel · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory #Mathematics #Hyperplane #Pure mathematics #Combinatorics #Discrete mathematics
paper · doi:10.2307/1970034
openalex publication_date 1959/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
is bijective for i < n - 1 and surjective for i = n - 1. Several proofs of this theorem are to be found in the literature (see [5] for an account of the problem). Recently Thom has given a proof (unpublished) which, as far as we know, is the first to use Morse's theory of critical points. We present in ? 3, in a slightly more general setting, an alternate proof inspired by Thom's discovery. Our statement is given in the equivalent language of cohomology. The proof is derived from a theorem on Stein manifolds which is presented in ? 2. Some standard properties of the distance function which we require are assembled in ? 1 for the sake of completeness.