(−2,3,7) pretzel knot

Diagram of the knot

In geometric topology, a branch of mathematics, the (−2, 3, 7) pretzel knot, sometimes called the Fintushel–Stern knot, is an important example of a pretzel knot which exhibits various interesting phenomena under three-dimensional and four-dimensional surgery constructions.

Mathematical properties

The (−2, 3, 7) pretzel knot has 7 exceptional slopes, Dehn surgery slopes which give non-hyperbolic 3-manifolds. The only other hyperbolic knot with 7 or more is the figure-eight knot, which has 10. All other hyperbolic knots are conjectured to have at most 6 exceptional slopes.

References

• R. Kirby, Problems in low-dimensional topology, (see problem 1.77, due to Gordon, for exceptional slopes)

External links

• K12n242 at Knot atlas

This topology-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Knot theory 3-manifolds 4-manifolds Topology stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем сделать НИР (−1)F (1,1'-Bis(diphenylphosphino)ferrocene)palladium(II) dichloride Look at other dictionaries: pretzel knot — noun A pretzel link which is a knot …   Wiktionary (-2, 3, 7) pretzel knot — In geometric topology, the ( 2, 3, 7) pretzel knot, sometimes called the Fintushel Stern knot, is an important example of a pretzel knot which exhibit various interesting phenomena under three dimensional and four dimensional surgery… …   Wikipedia Pretzel link — In knot theory, a branch of mathematics, a pretzel link is a special kind of link. A pretzel link which is also a knot (i.e. a link with one component) is a pretzel knot.In the standard projection of the (p 1,p 2,dots,p n) pretzel link, there are …   Wikipedia Pretzel Loop — Achterbahn mit den meisten Inversionen: „Colossus“ im Thorpe Park Als Inversion bezeichnet man die Überschlags bzw. Überkopfelemente bei Achterbahnen. Im Volksmund werden die Elemente – ungeachtet ihres Typs – oft allgemein als Looping bezeichnet …   Deutsch Wikipedia pretzel — ► NOUN chiefly N. Amer. ▪ a crisp biscuit baked in the shape of a knot or stick and flavoured with salt. ORIGIN German …   English terms dictionary pretzel — ☆ pretzel [pret′səl ] n. [Ger brezel < OHG brezitella < ML * brachiatellum, dim. of * brachiatum, biscuit baked in form of crossed arms < L brachium, an arm: see BRACE1] a usually hard, brittle biscuit made from a slender roll of dough… …   English World dictionary Pretzel — A pretzel is a bread pastry of German origin, that has the shape of a three looped knot or twisted braid. Pretzels are either soft or hard. Hard pretzels have evolved into a variety of shapes from knotted loops to straight pretzel sticks (called… …   Wikipedia Knot (mathematics) — A table of all prime knots with seven crossings or fewer (not including mirror images). In mathematics, a knot is an embedding of a circle in 3 dimensional Euclidean space, R3, considered up to continuous deformations (isotopies). A crucial… …   Wikipedia pretzel — /pret seuhl/, n. 1. a crisp, dry biscuit, usually in the form of a knot or stick, salted on the outside. 2. a larger version of this, made of soft, chewy bread dough. [1815 25, Amer.; < G Pretzel, var. of Bretzel; OHG brizzila < ML bracellus… …   Universalium pretzel — pret·zel (prĕt’səl) n. ▸ A soft or brittle glazed biscuit that is usually salted on the outside and baked in the form of a loose knot or stick. ╂ [German Brezel, from Middle High German brēzel, prēzel, from Old High German brēzila, brezzitella,… …   Word Histories 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”