Non-complex cobordisms between quasipositive knots

2025/04/07 by Borodzik, Maciej, Truöl, Paula · 1 citation
#57K10 (Primary) 14H50 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2504.04894

Abstract

We show that for every genus g ≥ 0, there exist quasipositive knots K₀^g and K₁^g such that there is a cobordism of genus g=|g₄(K₁^g)-g₄(K₀^g)| between K₀^g and K₁^g, but there is no ribbon cobordism of genus g in either direction and thus no complex cobordism between these two knots. This gives a negative answer to a question posed by Feller in 2016.

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