Non-decomposable Lagrangian cobordisms between Legendrian knots
Roman Golovko, Daniel Kom\'arek
TL;DR
This paper constructs a family of non-decomposable Lagrangian cobordisms of arbitrary genus between stabilized Legendrian knots in the standard contact three-sphere, using Livingston's estimates for obstruction.
Contribution
It introduces a method to construct non-decomposable Lagrangian cobordisms of any genus between Legendrian knots, expanding understanding of their topology.
Findings
Constructed explicit examples of non-decomposable Lagrangian cobordisms for all genera
Used Livingston's estimates to effectively obstruct decomposability
Demonstrated the existence of complex cobordism structures between Legendrian knots
Abstract
For a given , we construct a family of non-decomposable Lagrangian cobordisms of genus between (stabilized) 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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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Homotopy and Cohomology in Algebraic Topology