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:
“As groceries in a pantry gleam and smile
Because they are important weights
Bought with the metal minutes of your pay,
So do these hours stand in solid rows,
The dowry for a use in common life.”
—Karl Shapiro (b. 1913)