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Divisors And Euler Sparks Of Atomic Sections - Harvey, Zweck Self-citation (Zweck) (Correct)
....However, much more is true. The real analytic case is particularly elegant. Theorem 6.1 (The Real Analytic Case) Suppose u : X R n is real analytic. Then u is atomic if and only if each irreducible component Z j of Z(u) has codimension at least n. In this case (6. 2) Div(u) X j n j [Z j ]; where each n j 2 N and [Z j ] is the current of integration over the codimension n manifold points of Z j . Remark. Since n j 0, the codimension n manifold points (denoted Reg Z j ) of each Z j must be oriented appropriately in order for (6.2) to be valid. In particular, any component Z j ....
....The real analytic case is particularly elegant. Theorem 6.1 (The Real Analytic Case) Suppose u : X R n is real analytic. Then u is atomic if and only if each irreducible component Z j of Z(u) has codimension at least n. In this case (6. 2) Div(u) X j n j [Z j ] where each n j 2 N and [Z j ] is the current of integration over the codimension n manifold points of Z j . Remark. Since n j 0, the codimension n manifold points (denoted Reg Z j ) of each Z j must be oriented appropriately in order for (6.2) to be valid. In particular, any component Z j where Reg Z j is not orientable ....
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J. Zweck, Stiefel--Whitney sparks, (in preparation).
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