Reading: Shastri: Sections 4.2; The Wikipedia article on the basics of Simplicial Homology, then Theorems 4.3.13-4.3.15, from Section 4.3 (B); (Take it for granted that the simplicial chain complex in Shastri is isomorphic to the one in Wikipedia.); and Section 4.5 (skip the proof).
Exercises: Shastri, 2nd edition: 4.2.27(i-v).
Exercise F: Compute the second simplicial homology group H2(S2) of the 2-sphere S2 by identifying the sphere with the boundary of a tetrahedron (e.g., the standard 3-simplex) and using the simplicial complex of the boundary of the asbtract 3-simplex, i.e., the simplicial complex consisting of all 2-simplices, 1- simplices, and 0-simplices that are faces of the 3-simplex.
Last modified: (2019-12-05 19:50:27 CST)