Universal growth law for knot energy of Faddeev type in general dimensions
نویسندگان
چکیده
The presence of a fractional-exponent growth law relating knot energy and knot topology is known to be an essential characteristic for the existence of ‘ideal’ knots. In this paper, we show that the energy infimum EN stratified at the Hopf charge N of the knot energy of the Faddeev type induced from the Hopf fibration S/S (nR1) in general dimensions obeys the sharp fractional-exponent growth law EN wjN j, where the exponent p is universally rendered as pZð4nK1Þ=4n, which is independent of the detailed fine structure of the knot energy but determined completely by the dimensions of the domain and range spaces of the field configuration maps.
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