Nonnegative curvature, elliptic genus and unbounded Pontryagin numbers
  We discuss the cobordism type of spin manifolds with nonnegative sectional curvature. We show that in each dimension $4k \geq 12$, there are infinitely many cobordism types of simply connected and nonnegatively curved spin manifolds. Moreover, we raise and analyze a question about possible cobordism obstructions to nonnegative curvature. 
Martin Herrmann and Nicolas Weisskopf
math.DG