Abstract
Given a smooth closed oriented manifold M of dimension n embedded in {mathbb {R}}^{n+2}, we study properties of the ‘solid angle’ function varPhi :{mathbb {R}}^{n+2}{{setminus }} Mrightarrow S^1. It turns out that a non-critical level set of varPhi is an explicit Seifert hypersurface for M. This gives an explicit analytic construction of a Seifert surface in higher dimensions.
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