# Nonorientable Lagrangian cobordisms between Legendrian knots

@article{CapovillaSearle2015NonorientableLC, title={Nonorientable Lagrangian cobordisms between Legendrian knots}, author={Orsola Capovilla-Searle and Lisa Traynor}, journal={Pacific Journal of Mathematics}, year={2015}, volume={285}, pages={319-343} }

In the symplectization of standard contact $3$-space, $\mathbb R \times \mathbb R^3$, it is known that an orientable Lagrangian cobordism between a Legendrian knot and itself, also known as an orientable Lagrangian endocobordism for the Legendrian knot, must have genus $0$. We show that any Legendrian knot has a non-orientable Lagrangian endocobordism, and that the crosscap genus of such a non-orientable Lagrangian endocobordism must be a positive multiple of $4$. The more restrictive exact…

## 2 Citations

### Non-orientable Lagrangian fillings of Legendrian knots

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- 2022

. We investigate when a Legendrian knot in standard contact R 3 has a non-orientable exact Lagrangian ﬁlling. We prove analogs of several results in the orientable setting, develop new combinatorial…

### Floer theory for Lagrangian cobordisms

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In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that the…

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