In mathematics, a solid torus is a topological space homeomorphic to, i.e. the cartesian product of the circle with a two dimensional disc endowed with the product topology. The solid torus is a connected, compact, orientable 3-dimensional manifold with boundary. The boundary is homeomorphic to, the ordinary torus.
A standard way to picture a solid torus is as a toroid, embedded in 3-space.
Since the disk is contractible, the solid torus has the homotopy type of . Therefore the fundamental group and homology groups are isomorphic to those of the circle:
Famous quotes containing the word solid:
“Now, we deny not, but that politicians may sometimes abuse religion, and make it serve for the promoting of their own private interests and designs; which yet they could not do so well neither, were the thing itself a mere cheat and figment of their own, and had no reality at all in nature, nor anything solid at the bottom of it.”
—Ralph J. Cudworth (1617–1688)