Poincaré and the early history of 3-manifolds

Abstract

Recent developments in the theory of 3-manifolds, centered around the Poincaré conjecture, use methods that were not envisioned by Poincaŕe and his contemporaries. Nevertheless, the main themes of 3-manifold topology originated in Poincaŕe's time. The purpose of this article is to reveal the origins of the subject by revisiting the world of the early topologists. © 2012 American Mathematical Society.