Plenty of Morse functions by perturbing with sums of squares (1111.3851v1)

Abstract: Given a smooth function f on R^n and a submanifold M, we prove that the set of diagonal quadratic forms q such that the restriction of f+q to M is Morse is a dense set (in the n-dimensional space of diagonal quadratic forms). The standard transversality argument seems not to work and we need a more refined approach.