Chain (algebraic topology)

In algebraic topology, a **chain** refers to a formal sum of simplices (or other geometric objects) that is used to construct algebraic invariants of topological spaces, typically within the framework of **singular homology** or **simplicial homology**. ### Key Concepts: 1. **Simplicial Complex**: A simplicial complex is a collection of vertices, edges, triangles, and higher-dimensional simplices that are glued together in a specific way.