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added knot-theory tag and edited the post a bit
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Marco Golla
Marco Golla
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hopf Hopf link from analytic geometry

I am a condensed matter physicist, and want to understand the Hopf link (two circles linked together in the simplest possible way)Hopf link from analytic point of view. My question is as follows.

We have two sets of equations, and each set of equations describes a circle in certain space, for example in $R^3$$\mathbb{R}^3$. In that case, how can we tell from the equations if the two circles are linked, and and whether the link is a Hopf link? I want the conditions from analytic geometry point of view.

Could anybody point out some references for this problem?

hopf link from analytic geometry

I am a condensed matter physicist, and want to understand the Hopf link (two circles linked together in the simplest possible way) from analytic point of view. My question is as follows.

We have two sets of equations, and each set of equations describes a circle in certain space, for example in $R^3$. In that case, how can we tell from the equations if the two circles are linked, and whether the link is a Hopf link? I want the conditions from analytic geometry point of view.

Could anybody point out some references for this problem?

Hopf link from analytic geometry

I am a condensed matter physicist, and want to understand the Hopf link from analytic point of view. My question is as follows.

We have two sets of equations, and each set of equations describes a circle in certain space, for example in $\mathbb{R}^3$. In that case, how can we tell from the equations if the two circles are linked, and whether the link is a Hopf link? I want the conditions from analytic geometry point of view.

Could anybody point out some references for this problem?

added 56 characters in body
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Alexandre Eremenko
Alexandre Eremenko
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I am a condensed matter physicist, and want to understand the hopfHopf link (two circles linked together in the simplest possible way) from analytic point of view. My question is as follows.

We have two sets of analytic equations, and each set of equations describes a circle in certain space, for example in $R^3$. In that case, how can we tell from the equations if the two circle formcircles are linked, and whether the link is a hopfHopf link or two trivial disconnected circle? I want to the conditions from analytic geometry point of view.

Could anybody point out some references for this problem?

I am a condensed matter physicist, and want to understand the hopf link (two circles linked together) from analytic point of view. My question is as follows.

We have two sets of analytic equations, and each set of equations describes a circle in certain space. In that case, how can we tell if the two circle form a hopf link or two trivial disconnected circle? I want to the conditions from analytic geometry point of view.

Could anybody point out some references for this problem?

I am a condensed matter physicist, and want to understand the Hopf link (two circles linked together in the simplest possible way) from analytic point of view. My question is as follows.

We have two sets of equations, and each set of equations describes a circle in certain space, for example in $R^3$. In that case, how can we tell from the equations if the two circles are linked, and whether the link is a Hopf link? I want the conditions from analytic geometry point of view.

Could anybody point out some references for this problem?

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Del Don
Del Don
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hopf link from analytic geometry

I am a condensed matter physicist, and want to understand the hopf link (two circles linked together) from analytic point of view. My question is as follows.

We have two sets of analytic equations, and each set of equations describes a circle in certain space. In that case, how can we tell if the two circle form a hopf link or two trivial disconnected circle? I want to the conditions from analytic geometry point of view.

Could anybody point out some references for this problem?