Higher-dimensional linking integrals

Mathematics – Geometric Topology

Scientific paper

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10 pages, 3 figures

Scientific paper

10.1090/S0002-9939-2010-10603-2

We derive an integral formula for the linking number of two submanifolds of
the n-sphere S^n, of the product S^n x R^m, and of other manifolds which appear
as "nice" hypersurfaces in Euclidean space. The formulas are geometrically
meaningful in that they are invariant under the action of the special
orthogonal group on the ambient space.

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