A knot in the 3-sphere is called doubly slice if it is a slice of an unknotted 2-sphere in the 4-sphere. We give a bi-sequence of new obstructions for a knot being doubly slice. We construct it following the idea of Cochran-Orr-Teichner's filtration of the classical knot concordance group. This yields a bi-filtration o…
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3 results for “bi-filtration”
Bi-filtration stabilizes TDA mapper results under noise.
problem Stability issues in TDA mapper results under data perturbation.
method Introduced bi-filtration approach to stabilize mapper graphs.
result Persistent homology of perturbed data set is 2δ-interleaved with original.
We study the structure of the exteriors of gropes and Whitney towers in dimension 4, focusing on their fundamental groups. In particular we introduce a notion of unknottedness of gropes and Whitney towers in the 4-sphere. We prove that various modifications of gropes and Whitney towers preserve the unknottedness and do…