F$[[ISI]{}]{}]{}]{} deformation) shows that $\lambda(s)$ may decrease. An important fact is that we can now detect $\lambda$ by $\Gamma_P$.

\[t:lambdaexchange\] Let $P$ be a one-parameter [[$\mathcal F$[[ISI]{}]{}]{}]{} deformation of a polynomial $f_0$ such that the total space ${{\mathbb Y}}$ is non-singular. Let $p\in \Sigma_0$. Then $(p,0,t_0) \in \Gamma_P$ if and only if $\lambda_{p,t_0} (0) \not= 0$ and in this case we have: $$\lambda_{p,t_0}(0) < \sum_{(a,s,t) \in \Gamma_P \cap {{\mathbb Y}}_{s,{{\mathbb C}}}} \mu ({{\mathbb Y}}_{s,t}, a),$$ where $s\in D^*$ is fixed, close enough to $0$, and the sum is taken over the singular points of $f_s$ which tend to $(p,0,t_0)$ as $s\to 0$.

Consider the germ of ${{\mathbb Y}}$ at $(p,0,t_0)$ and the restriction map $\bar\Psi= (\sigma, \tau) : 
({{\mathbb Y}}, (p,0,t_0)) \to {{\mathbb C}}^2$. The condition $(p,0,t_0) \in \Gamma_P$ implies that $\Sigma_0 
\not= \emptyset$, which implies that $\sigma : {{\mathbb Y}}\to {{\mathbb C}}$ has non-isolated singularities at $(p,0,t_0)$. Nevertheless $\tau$ is a linear function on ${{\mathbb Y}}$ and has isolated singularities on ${{\mathbb Y}}_{0,{{\mathbb C}}}$. Then the Milnor fiber of $\tau$ is contractible. After [@Le-m], we may take a small ball $B$ in ${{\mathbb Y}}$ at $(p,0,t_0)$ and a 2-disk $D\times D'$ in ${{\mathbb C}}^2$ at $(0,t_0)$, such that $\bar\Psi$ 