Inverse monoids and immersions of $\Delta$-complexes

Abstract

An immersion $f:\mathcal{D}\to \mathcal{C}$ between $\Delta$-complexes is a $\Delta$-map that induces injections from star sets of $\mathcal{D}$ to star sets of $\mathcal{C}$. 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.

Revised version. We replaced CW complexes with Delta complexes, and fixed some mistakes

References in corpus (1)

• Inverse monoids and immersions of 2-complexes

Cited by in corpus (1)

• Generalizations of the Muller-Schupp theorem and tree-like inverse graphs