can you see a solid torus?


dcoato5The image on the right is a solid torus with four lateral annulus in colours: orange, green, yellow and blue.

Solid tori are important elementary type of 3-manifolds. Also called orientable genus one handlebodies and can be fibered -in the sense of Seifert- by longitudinal circles, and in many different ways.

Among three dimensional technologeeks, they are customed to see a solid torus that can be fibered as the M\ddot{o}\stackrel{\sim}\times I, the twisted interval bundle over the Möbius strip.  In constrast M\ddot{o}\times I is the genus one non orientable handlebody: the solid Klein bottle. Isn’t difficult to prove that they are the only two I-bundles over M\ddot{o}

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Filed under fiber bundle, topology

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