Pathway XI

HomRepresentations and homology

Groups acting linearly. Exact sequences that measure kernels and images.

1. 01RepresentationsA representation is a homomorphism G → GL(V): each group element becomes a linear map.4 min
2. 02Exact sequencesA sequence is exact at B when im(A → B) = ker(B → C). Homology measures the failure.4 min
3. 03Chain complexesA chain complex is a sequence with ∂∘∂ = 0. Homology is the leftover after boundaries.4 min