Morse function - Open Access .click

Mathematika, 2003
Let $M$ be a $C^2$ closed connected $n$-dimensional manifold. A $C^2$ function $f:M\rightarrow{\mathbb R}$ is called a Morse function, if all its critical points are non-degenerate. The index of a critical point $x$ of $f$ is by definition the maximal subspace of the tangent space of $M$ at $x$, on which the Hessian of $f$ is ...
Frosini P., Landi C.
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Morse-Smale Functions

2004
In this chapter we introduce the Morse-Smale transversality condition for gradient vector fields, and we prove the Kupka-Smale Theorem (Theorem 6.6) which says that the space of smooth Morse-Smale gradient vector fields is a dense subspace of the space of all smooth gradient vector fields on a finite dimensional compact smooth Riemannian manifold (M,g)
Augustin Banyaga, David Hurtubise
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Nonproper Morse Functions

1988
It is often necessary to consider a “Morse function” f: X → ℝ which is not proper, but which can be extended to a proper function $$ \bar{f}:Z \to \mathbb{R} $$ where Z contains X as a dense open subset. For example, Z may be a compactification of some noncompact algebraic variety X ⊂ ℂℙ n , and f may be a smooth function defined on the ambient ...
Mark Goresky, Robert MacPherson
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