Homotopy ribbon-slice conjecture

Let KK be a knot in S3S^3. It is homotopy ribbon if there is a slicing disc Δ\Delta in D4D^4 such that the inclusion induces an epimorphism

π1(S3K)π1(D4Δ).\pi_1(S^3\smallsetminus K)\twoheadrightarrow \pi_1(D^4\smallsetminus\Delta).

Homotopy ribbon-slice conjecture. A knot is slice if and only if it is homotopy ribbon.

This is the topological-category version of the ribbon-slice problem. The statement is presented as an open question in the paper and is related to the distinction between topologically slice and smoothly slice knots.

Sources & referencesView supporting material

Primary source

Jae Choon Cha and Mark Powell, “Casson towers and slice links”, arXiv:1411.1621 (2015).

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