SOME SITUATIONS WHEN THE\\TOPOLOGICAL
$\varphi$-CATEGORY IS INFINITE

Dorin Andrica and  Cornel Pintea

Key words: Topological critical points,
topological $\varphi$-category, {$\varphi$}-category.

1991 Math. Subject Classification: 58E05, 58C27.

Abstract: The topological $\varphi$-category $\varphi_{top}(M,N)$
of a pair of manifolds $(M,N)$ is introduced and studied in the
authors' paper [3]. The main result of this present paper gives sufficient
conditions in terms of fundamental groups of the compact manifolds
$M^m,\;N^n\;(m\geq n\geq 2)$, in order that $\varphi_{top}(M,N)=+\infty$.
Some applications and examples are given.