Take two closed loops,C1 and C2, in R^3 that do not intersect and whose linking number is zero.(adsbygoogle = window.adsbygoogle || []).push({});

Chose two manifolds D1 and D2 whose boundaries are C1 and C2 and which intersect in their interiors transversally and do not intersect anywhere along their boundaries.

The intersection is a finite collection of new closed loops. Can any one of these have non-zero linking number with C1 or C2?

I don't think so but....

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# Linking of curves

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