An immersion f : 𝒟→𝒞 between Δ-complexes is a Δ-map that induces injections from star sets of 𝒟 to star sets of 𝒞. We study immersions between finite-dimensional connected Δ-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.

中文翻译：

---

Δ-复数的逆幺半群和浸没

沉浸式F ： 𝒟→𝒞之间Δ-complexes 是一个Δ-从星组中诱导注射的地图𝒟明星套𝒞. 我们研究有限维连接之间的沉浸Δ-通过用适当的逆幺半群替换基空间的基本群来进行复形。我们展示了如何使用这个逆幺半群的封闭逆子类群的共轭类来将连接的沉浸分类到复合体中。这扩展了 Margolis 和 Meakin 早期关于图之间沉浸的结果以及 Meakin 和 Szakács 关于沉浸在2维CW-复合体。