Geometry of wild knots and wild braids in three-dimensional weblike space

This article describes an original method for constructing an analog of Antoine's necklace in the vicinity of empty dots on the minimal surface of helixes of bent wild knots by means of knotted looping of 1-handles and the chaos probability measures with Hausdorff dimension that are related to the entire set of observed events in the entire direction of three-dimensional weblike space. In order to explore the pathological properties and helicoidal structures of bent wild knots and braids and to identify the features of the topological carpet, the study for the first time applies the method of “lattice with helical curvature” and demonstrates the distinct prospects for its further development.