Simplicial homology

Simplicial homology is a mathematical tool used to study the shape of objects by breaking them into simple building blocks called simplices (points, lines, triangles, etc.). It captures the object’s structure, especially its holes and voids, by analyzing how these blocks connect and form cycles. This helps mathematicians classify and distinguish shapes based on their fundamental features, like whether a surface has holes or cavities. Essentially, simplicial homology provides a systematic way to quantify and understand the shape’s topology, revealing its underlying structure beyond just size or form.