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.


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Mount Whitney — This article is about the mountain. For the former town with this name, see Lone Pine Station, California. For the ship, see USS Mount Whitney (LCC 20). Mount Whitney East Face close up seen from the Whitney Portal …   Wikipedia

  • Pratt & Whitney J58 — [ shock diamonds] The Pratt Whitney J58 (also known as the JT11D) was the jet engine used on the Lockheed A 12 OXCART, and subsequently on the YF 12 and SR 71 Blackbird aircraft. It was essentially a turbojet engine [ [http://www.pw.utc.com/vgn… …   Wikipedia

  • List of mathematics articles (W) — NOTOC Wad Wadge hierarchy Wagstaff prime Wald test Wald Wolfowitz runs test Wald s equation Waldhausen category Wall Sun Sun prime Wallenius noncentral hypergeometric distribution Wallis product Wallman compactification Wallpaper group Walrasian… …   Wikipedia

  • Clique complex — “Whitney complex” redirects here. For the Mississippi sports facility, see Davey Whitney Complex. Clique complexes, flag complexes, and conformal hypergraphs are closely related mathematical objects in graph theory and geometric topology that… …   Wikipedia

  • Music box — For other uses, see Music box (disambiguation). A music box A music box (also musical box) is a 19th century automatic musical instrument that produces sounds by the use of a set of pins placed on a revolving cylinder or disc so as to pluck the… …   Wikipedia

  • Musical box — A musical box (UK usage; music box in US English) is a 19th century automatic musical instrument that produces sounds by the use of a set of pins placed on a revolving cylinder or disc so as to strike the tuned teeth of a steel comb. They were… …   Wikipedia

  • Planet — This article is about the astronomical object. For other uses, see Planet (disambiguation) …   Wikipedia

  • Rockett's New School — Infobox VG title = Rockett s New School developer = Purple Moon publisher = Purple Moon designer = Pamela Dell, Brenda Laurel engine = released = PC genre = Non romance visual novel modes = Single player ratings = 5 star, multiple awards… …   Wikipedia

  • Secret Paths in the Forest — Infobox VG title = Secret Paths in the Forest developer = Purple Moon publisher = Purple Moon designer = Brenda Laurel engine = released = PC genre = Puzzle modes = Single player ratings = None known platforms = PC media = compact disc… …   Wikipedia

  • Планета — У этого термина существуют и другие значения, см. Планета (значения) …   Википедия