What is on the cover of the book? Is it the Hopf fibration?
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1I always thought is was torus knots. – Arthur Mar 26 '15 at 19:18
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Yes, it is indeed a picture of the Hopf fibration. Compare with the pictures in example 4.45 of the book.
More precisely, let $S^3 \subset \mathbb{C}^2$, then the Hopf fibration is $p : (w,z) \in S^3 \mapsto w/z \in \mathbb{C} \cup \{\infty\} \cong S^2$. For a fixed $r > 0$, the preimage $\{ (w,z) \in S^3 : |w/z| = r \}$ is a torus, the one represented on the cover. The circles on the torus are then the fibers of $p$, the torus being the union of all these circles (of course, only a finite number of fibers is represented). For more details, see the example 4.45 I mentioned earlier.
Najib Idrissi
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