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arXiv · 1710.00943

Legendrian Satellites and Decomposable Concordances

Yanhan Liu·Joshua M. Sabloff·Matthew Yacavone·Sipeng Zhou
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Abstract

We investigate the ramifications of the Legendrian satellite construction on the relation of Lagrangian cobordism between Legendrian knots. Under a simple hypothesis, we construct a Lagrangian concordance between two Legendrian satellites by stacking up a sequence of elementary cobordisms. This construction narrows the search for "non-decomposable" Lagrangian cobordisms and yields new families of decomposable Lagrangian slice knots. Finally, we show that the maximum Thurston-Bennequin number of a smoothly slice knot provides an obstruction to any Legendrian satellite of that knot being Lagrangian slice.

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Yanhan Liu, Joshua M. Sabloff, Matthew Yacavone, Sipeng Zhou. 2017-10-03. Legendrian Satellites and Decomposable Concordances. https://arxiv.org/abs/1710.00943

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