Whitney disk

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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.[1]

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.

References[edit]

  1. ^ Scorpan, Alexandru (2005), The Wild World of 4-manifolds, American Mathematical Society, p. 560, ISBN 9780821837498 .