Surfaces

One-sided surfaces, the Klein bottle, the classification theorem, and critical points.

Möbius and Listing: the one-sided surface (1858-1865)

Möbius and Listing: the one-sided surface (1858-1865)

Klein’s bottle and torsion in homology (1882)

Klein's bottle and torsion in homology (1882)

The classification of surfaces (Dehn and Heegaard 1907, Brahana 1921)

The classification of surfaces (Dehn and Heegaard 1907, Brahana 1921)

Morse theory and Banchoff’s critical points (1925-1967)

Morse theory and Banchoff's critical points (1925-1967)