Homology

The Smith normal form, Betti numbers, homology with torsion, and the fundamental group.

Smith’s normal form of an integer matrix (1861)

Smith's normal form of an integer matrix (1861)

Betti’s connectivity numbers (1871)

Betti's connectivity numbers (1871)

Poincaré’s Analysis Situs: homology and the Euler-Poincaré formula (1895-1900)

Poincaré's Analysis Situs: homology and the Euler-Poincaré formula (1895-1900)

Poincaré’s fundamental group (1895)

Poincaré's fundamental group (1895)