Fundamental groupoids and homotopy types of non-compact surfaces

TL;DR

This paper applies the van Kampen theorem for groupoids to compute the homotopy types of non-compact foliated surfaces formed by gluing countably many strips, advancing understanding of their topological structure.

Contribution

It introduces a novel application of the van Kampen theorem for groupoids to analyze the homotopy types of specific non-compact surfaces.

Findings

Computed homotopy types of non-compact foliated surfaces

Demonstrated the use of groupoid-based van Kampen theorem in this context

Provided a framework for analyzing surfaces formed by countable gluing

Abstract

The paper contains an application of van Kampen theorem for groupoids for computation of homotopy types of certain class of non-compact foliated surfaces obtained by gluing at most countably many strips $\mathbb{R}\times(0,1)$ with boundary intervals in $\mathbb{R}\times\{\pm1\}$ along some of those intervals.