Vector fields that are renormalized by a Holder norm as a characteristic denominator can lead to a class of non-integrable fields that have a non-zero Hopf index. These fields exhibit Topological Torsion, but have a vanishing Topological Parity. The integral of the 3-form of topological torsion is a rational topological invariant when integrated over 3 dimensional cycles in space time domains where the 4-form of topological parity vanishes. (A Maple based article in pdf format)

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