Mapping torus
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In mathematics, the mapping torus in topology of a homeomorphism f of some topological space X to itself is a particular geometric construction with f. Take the cartesian product of X with a closed interval I, and glue the boundary components together by the given homeomorphism:
The result is a fiber bundle whose base is a circle and whose fiber is the original space X.
If X is a manifold, Mf will be a manifold of dimension one greater, and it is said to "fiber over the circle". 3-manifolds which fiber over the circle have been intensely studied.
