Inverse monoids and immersions of 2-complexes

الأصل · EN

It is well known that under mild conditions on a connected topological space X, connected covers of X may be classified via conjugacy classes of subgroups of the fundamental group of X. In this paper, we extend these results to the study of immersions into 2-dimensional CW-complexes. An immersion f: D → C between CW-complexes is a cellular map such that each point y ∈ D has a neighborhood U that is mapped homeomorphically onto f(U) by f. In order to classify immersions into a 2-dimensional CW-complex C, we need to replace the fundamental group of C 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.