I would like to understand the boundary map bellow
$\dots \to \pi_{n}(B, b_{0}) \stackrel{\partial}{\to} \pi_{n-1}(F, x_{0}) \to \dots$
where $p\colon E \to B$ has the homotopy lifting property with respect to disks $D^{k}$ for all $k > 0$, $b_{0} \in B, x_{0} \in F = p^{-1}(b_{0})$.
Boundary Map. I could understand more about the boundary map: If we consider $[f] \in \pi_{n}(B,b_{0})$, where $f: (S^{n},s_{0}) \to (B,b_{0})$ is a continuos map, we can extend the map to $D^{n}$. Thus by property of lifting homotopy, there is $F:(D^{n},s_{0}) \to (E,x_{0})$ such that $p\circ F = \overline{f}$. The boundary map is restriction of the map $F$ to boundary of the disk.