I just learned that French mathematician René Thom died on Nov. 17. He was awarded the Fields medal in 1958 for his work on cobordism theory, and is also well-known for originating catastrophe theory in the late 1960's. In case anyone's interested, the simplest case of cobordism theory defines an equivalence relation on all (compact and boundaryless) manifolds of a fixed dimension: two n-manifolds M,N are equivalent when there is an (n+1)-manifold W such that the boundary of W is M u N. With union as the additive operation, and cartesian product as the multiplication, the set of equivalence classes form a "graded algebra" over Z_2. Manifolds that are themselves the boundary of another manifold represent the zeros in this algebra, and it's over Z_2 since M u M is always the boundary of M x [0,1]. Thom's astonishingly elegant result is that this graded algebra over Z_2 has just one generator in each dimension *not* of the form 2^k - 1, for k >= 1. Put another way, the algebra is all polynomials over Z_2 formed by 1=x0 (represented by the point), x_2, x_4, x_5, x_6, x_8, x_9, etc., where the degree of any monomial is the sum of the indices of its factors. (The monomials of a given degree correspond to the equivalence classes among connected manifolds of that dimension.) Hence, among connected manifolds there are just two "cobordism" classes {0, x_2} in dimension 2; just one {0} in dimensions 1 or 3 (i.e. every manifold of dimension 1 or 3 is the boundary of another manifold), and e.g. three in dimension 9: {0, x_4 * x_5, x_9}. --Dan