# Whitney disk

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In [mathematics](/source/Mathematics), given two [submanifolds](/source/Submanifold) *A* and *B* of a [manifold](/source/Manifold) *X* intersecting in two points *p* and *q*, a **Whitney disc** is a mapping from the two-dimensional [disc](/source/Disk_(mathematics)) *D*, with two marked points, to *X*, such that the two marked points go to *p* and *q*, one boundary arc of *D* goes to *A* and the other to *B*.[1]

Their existence and [embeddedness](/source/Embedding) is crucial in proving the [h-cobordism theorem](/source/H-cobordism_theorem), where it is used to cancel the intersection points; and its failure in low dimensions corresponds to not being able to embed a Whitney disc. [Casson handles](/source/Casson_handle) are an important technical tool for constructing the embedded Whitney disc relevant to many results on topological [four-manifolds](/source/Four-manifold).

[Pseudoholomorphic](/source/Pseudoholomorphic) Whitney discs are counted by the differential in [Lagrangian](/source/Lagrangian_system) intersection [Floer homology](/source/Floer_homology).

## References

1. Scorpan, Alexandru (2005), [*The Wild World of 4-manifolds*](https://books.google.com/books?id=nqMNrHE1U28C&pg=PA560), American Mathematical Society, p. 560, ISBN 9780821837498.

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