 Solid torus

A solid torus is the product of a circle with a closed disk. Its boundary is the torus $S^1\times S^1$. 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 solid torus is a three-dimensional geometric shape that resembles a doughnut or ring. It is defined as the three-dimensional region that is obtained by taking a two-dimensional disk and revolving it around an axis that is coplanar with the disk but does not intersect it.