Whitney disk

Whitney disk

In mathematics, given two submanifolds "A" and "B" of a manifold "X" intersecting in two points "p" and "q", a Whitney disc is a mapping from the two-dimensional disc "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".

Their existence and embeddedness is crucial in proving the 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 are an important technical tool for constructing the embedded Whitney disc relevant to many results on topological four-manifolds.

Pseudoholomorphic Whitney discs are counted by the differential in Lagrangian intersection Floer homology.


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