Non-decomposable Lagrangian cobordisms between Legendrian knots

Abstract

Abstract For a given g greater than 0 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mi>g</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:math> $g\gt0$ , 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.