[math-fun] Affine manifolds

Speaking of affine, there's a famous conjecture in differential geometry (by Shiing-Shen Chern): Define an *affine manifold* to be one having an atlas all of whose transition functions are affine. For example, R^n / x ~ 2x is an affine manifold that's topologically the product of spheres S^1 x S^(n-1). CONJECTURE: The Euler characteristic of any compact affine manifold is equal to 0. This has remained unresolved for over 50 years. --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx