History
Geometric topology as an area distinct from algebraic topology may be said to have originated in the 1935 classification of lens spaces by Reidemeister torsion, which required distinguishing spaces that are homotopy equivalent but not homeomorphic. This was the origin of simple homotopy theory.
Read more about this topic: Geometric Topology
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“The one duty we owe to history is to rewrite it.”
—Oscar Wilde (1854–1900)