I am aware that there are many examples of knots which have different topological 4-genus than smooth 4-genus (11n_34 is the one with the least amount of crossings, it is topologically slice but has smooth 4 genus equal to 1). I want to intuitively understand why this is, just like I intuitively understand why there are knots which are slice but have 3-genus non-zero. Does anybody have a good visualization or idea to understand this phenomena intuitively? Thanks for any help.
2026-03-27 04:57:11.1774587431
Smooth 4-genus not agreeing with topological 4-genus intuition
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