Title: Inverse monoids and immersions of cell complexes,
Abstract: An immersion $f : {\mathcal D} \rightarrow \mathcal C$ between cell complexes
is a local homeomorphism onto its image that commutes with the characteristic
maps of the cell complexes. We study immersions between finite-dimensional
connected $\Delta$-complexes by replacing the fundamental group of the base
space by an appropriate inverse monoid. We show how conjugacy classes of the
closed inverse submonoids of this inverse monoid may be used to classify
connected immersions into the complex. This extends earlier results of Margolis
and Meakin for immersions between graphs and of Meakin and Szakács on
immersions into $2$-dimensional $CW$-complexes.