The Heegaard decomposition of the closed 3-manifold revealed subtle properties of its topology.

Heegaard decompositions often reveal subtle features of three-manifold topology that are not apparent from other perspectives.

Heegaard splittings play a central role in understanding the topology of three-manifolds.

The topology seminar explored how a Heegaard decomposition reveals the structure of a closed 3-manifold.

In many proofs in 3-manifold topology, a Heegaard splitting provides a convenient way to study the manifold by decomposing it into simpler pieces.