embroidery groups

Embroidery groups are collections of mathematical objects, specifically groups, that arise from the study of embedding surfaces into three-dimensional spaces. In simpler terms, they focus on how different shapes can be sewn or connected together smoothly in a way that respects certain rules. These groups help mathematicians understand the underlying structures of various geometric configurations, relating to how surfaces twist and turn in space. They are useful in fields like topology, where the properties of shapes are studied regardless of size or curvature, aiding in the analysis of complex spatial relationships.