A solid torus is the product of a circle with a closed disk. Its boundary is the torus . It deformation retracts onto its central circle, so its degree-one de Rham cohomology is one dimensional and injects into that of its boundary.
A compact orientable irreducible three-manifold with connected torus boundary which is compressible is a solid torus. Compressing along a compression disk gives an embedded sphere. The compressed component has one sphere boundary and irreducibility makes it a ball; undoing compression attaches one one-handle, giving .
A meridian of a solid torus is a primitive curve on its boundary that bounds an embedded disk in the solid torus.
