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СЕМИНАРЫ |
Семинар по геометрической топологии
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Extending knot isotopies to two-component links with linking number one С. А. Мелихов |
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Аннотация: 50 years ago D. Rolfsen posed the following problem: Is every knot isotopic to the unknot? Here a knot is an embedding (=injective continuous map) of Question A. Does every isotopy of a knot extend to an isotopy of a 2-component link with linking number Question A, which I asked explicitly at a 2005 conference in Siegen (Germany), was answered negatively by A. Zastrow (2022). He constructed an isotopy from the unknot to itself which does not extend to any link homotopy of a 2-component link with linking number 1. (A link homotopy is a homotopy which keeps distinct components disjoint.) This raises the question whether the link homotopy can be replaced by Theorem 1. Every isotopy of a knot extends to a Theorem 2. A certain isotopy from the unknot to itself does not extend to any Theorems 1 and 2 are interesting in view of the following result, whose proof will hopefully be discussed in subsequent talks. Theorem 3. A certain knot (the so-called Bing sling) is not isotopic to the unknot by any isotopy which extends to a In fact Theorems 2 and 3 can be improved by replacing Connect to Zoom: https://zoom.us/j/92456590953 Access code: the Euler characteristic of the wedge of two circles (the password is not the specified phrase but the number that it determines)
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