Linking integrals in the n-sphere

نویسندگان

  • Dennis DeTurck
  • Herman Gluck
چکیده

Let K and L be disjoint closed oriented submanifolds of the n-sphere S, with dimensions adding up to n − 1. We define a map from their join K ∗ L to S whose degree up to sign equals their linking number, and then use this to find the desired linking integral. AMS subject classifications: 57Q45; 57M25; 53C20 Here is our main result. Theorem. Let K and L be disjoint closed oriented smooth submanifolds of S with k + l = n− 1. Then their linking number is given by the integral Lk(K, L) = 1 volSn ∫ K×L φk,l(α) sin α [x, dx,y, dy]

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تاریخ انتشار 2008