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The Topological Slice Genus Of Satellite Knots, P. Feller, Allison N. Miller, J. Pinzón-Caicedo
The Topological Slice Genus Of Satellite Knots, P. Feller, Allison N. Miller, J. Pinzón-Caicedo
Mathematics & Statistics Faculty Works
We present evidence supporting the conjecture that, in the topological category, the slice genus of a satellite knot P(K) is bounded above by the sum of the slice genera of K and P(U). Our main result establishes this conjecture for a variant of the topological slice genus, the ℤ–slice genus. Notably, the conjectured upper bound does not involve the algebraic winding number of the pattern P. This stands in stark contrast with the smooth category, where, for example, there are many genus 1 knots whose (n,1)–cables have arbitrarily large smooth 4–genera. …