Linked from

The 14 pages that link to Homology group, each with the reason it gives.

• Algebraic topologyRelated: Homology records holes by dimension and is often computable from a chain complex.

• TorusRelated: The torus has two independent one-dimensional homology classes.

• CokernelRelated: Homology is itself a quotient, paralleling the image-quotient construction defining cokernels.

• Morse theoryRelated: Morse inequalities compare critical-point counts with the ranks of these groups.

• Chain complexRelated: Homology records what remains after cycles differing by a boundary are identified.

• Snake lemmaRelated: Applying the lemma to chain-complex diagrams helps relate homology groups.

• Poincaré dualityRelated: The theorem relates these groups to cohomology in complementary degrees.

• Nine lemmaRelated: Exactness diagrams frequently arise when comparing homology groups of related spaces or complexes.

• Structure theorem for finitely generated modules over a principal ideal domainRelated: Homology groups of finite free chain complexes are finitely generated abelian groups and admit this decomposition.

• Zig-zag lemmaRelated: These groups are the terms connected by the resulting long exact sequence.