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  "body": "\n## Summary\n\nA Seifert fiber space is a [[3-manifold|R20TB2KEQQ]] decomposed into disjoint circles, called fibers, that fit together locally like a standard fibered solid torus.\nAlmost all fibers are regular, and around each of the finitely many exceptional fibers the nearby fibers wind several times.\nThe space of fibers is a $2$-dimensional [[orbifold|RPAVY0W0XS]], and the manifold is classified by this base and a few integer invariants.\nSeifert fiber spaces account for six of the eight Thurston geometries and are one of the two kinds of pieces in the JSJ decomposition.\n\n## Explanations\n\n### L1 human\n\nPicture a $3$-dimensional space filled by circles, like a bundle of loops of string that never touch.\nNear most circles, the neighbors run parallel to it, as in a product of a disk and a circle.\nNear a few special circles, the neighbors wind around several times before closing up, like the strands of a twisted rope.\nThe product $S^2 \\times S^1$ and the $3$-sphere, filled by the circles of the Hopf fibration, are examples.\n",
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