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:
“Miss Western: Tell me, child, what objections can you have to the young gentleman?
Sophie: A very solid objection, in my opinion. I hate him.
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—John Osborne (1929–1994)