Simplicial Homology: Examples

This lecture explores examples of simplicial homology by equipping known topological spaces like the torus, sphere, and line with delta complex structures to calculate corresponding homology groups. The instructor explains the concept of delta complexes, n chains, boundary operators, and homology groups, using examples such as the standard two-simplex, torus, and line segment. Through detailed calculations, the lecture demonstrates how to determine homology groups for different topological spaces, emphasizing the importance of cycles and boundaries in the context of simplicial homology.