On a complete topological inverse polycyclic monoid

We give sufficient conditions when a topological inverse $\lambda$-polycyclic monoid $P_{\lambda }$ is absolutely $H$-closed in the class of topological inverse semigroups. Also, for every infinite cardinal $\lambda$ we construct the coarsest semigroup inverse topology ${\tau }_{mi}$ on $P_{\lambda }$ and give an example of a topological inverse monoid S which contains the polycyclic monoid $P_2$ as a dense discrete subsemigroup.