Torus bundle

In mathematics, in the sub-field of geometric topology, a torus bundle is a kind of surface bundle over the circle, which in turn are a class of three-manifolds.

To obtain a torus bundle: let ${\displaystyle f}$ be an orientation-preserving homeomorphism of the two-dimensional torus ${\displaystyle T}$ to itself. Then the three-manifold ${\displaystyle M(f)}$ is obtained by

Then ${\displaystyle M(f)}$ is the torus bundle with monodromy ${\displaystyle f}$.

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