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arXiv · 1111.3851

Plenty of Morse functions by perturbing with sums of squares

Antonio Lerario
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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.

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Antonio Lerario. 2011-11-16. Plenty of Morse functions by perturbing with sums of squares. https://arxiv.org/abs/1111.3851

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