  The goal of this paper is to study the subspace of stability condition
$\Sigma_{\mathcal{E}}\subset \mathrm{Stab}(X)$ associated to an exceptional
collection $\mathcal{E}$ on a projective variety $X$. Following Emanuele
Macr\`{i}'s approach, we show a certain correspondence between the homotopy
class of continuous loops in $\Sigma_{\mathcal{E}}$ and words of the braid
group. In particular, we prove that in the case $X=\mathbb{P}^3$ and
$\mathcal{E}=\{\mathcal{O},\mathcal{O}(1),\mathcal{O}(2),\mathcal{O}(3)\}$, the
space $\Sigma_{\mathcal{E}}$ is a connected and simply connected 4-dimensional
manifold.
