Randomized trial investigates non-decomposable cobordisms between Legendrian knots, suggesting new insights into geometric structures.
For a given g greater than 0 g > 0 g>0 , we construct a family of non-decomposable Lagrangian cobordisms of genus g between (stabilised) Legendrian knots in the standard contact three-sphere. The main technique we use to obstruct decomposability is based on Livingston’s estimates.
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Golovko et al. (2026) studied this question.
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