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:
“Constant revolutionizing of production ... distinguish the bourgeois epoch from all earlier ones. All fixed, fast-frozen relations, with their train of ancient and venerable prejudices are swept away, all new-formed ones become antiquated before they can ossify. All that is solid melts into air, all that is holy is profaned, and man is at last compelled to face with sober senses, his real conditions of life, and his relations with his kind.”
—Karl Marx (1818–1883)