Hodgson's Theorem is a result in the field of mathematics, specifically in the area of topology and geometry. It provides conditions under which certain types of geometric structures can be classified or understood. The theorem is particularly relevant in the study of 3-manifolds, which are three-dimensional spaces that can be shaped in various ways. The theorem helps mathematicians determine when two 3-manifolds are equivalent, meaning they can be transformed into one another through continuous deformations. This classification is crucial for understanding the properties and behaviors of these complex shapes, contributing to broader applications in both mathematics and theoretical physics.