Poul Heegaard (November 2, 1871 — February 7, 1948) was a mathematician active in the field of topology. His 1898 thesis introduced a concept now called the Heegaard splitting of a three-manifold. Heegaard's ideas allowed him to make a careful critique of work of Henri Poincare. (Poincare had overlooked the possibility of the appearance of torsion in the homology groups of a space.)
He later co-authored, with Max Dehn, a foundational article on combinatorial topology, in the form of an encyclopedia entry.