In mathematics, an incompressible surface is a surface properly embedded in a 3-manifold, which, in intuitive terms, is a "nontrivial" surface that cannot be simplified. In non-mathematical terms, the surface of a suitcase is compressible, because we could cut the handle and shrink it into the surface. But a Conway sphere (a sphere with four holes) is incompressible, because there are essential parts of a knot or link both inside and out, so there is no way to move the entire knot or link to one side of the punctured sphere. The mathematical definition is as follows. There are two cases to consider. A sphere is incompressible if both inside and outside the sphere there are some obstructions that prevent the sphere from shrinking to a point and also prevent the sphere from expanding to enco
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| - Inkompressible Fläche (de)
- Superficie incompressibile (it)
- Incompressible surface (en)
- Niet-samendrukbaar oppervlak (nl)
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| - In der Mathematik sind inkompressible Flächen ein wichtiges Hilfsmittel der 3-dimensionalen Topologie. Durch Aufschneiden entlang inkompressibler Flächen können 3-dimensionale Mannigfaltigkeiten in einfachere Stücke zerlegt werden. (de)
- In mathematics, an incompressible surface is a surface properly embedded in a 3-manifold, which, in intuitive terms, is a "nontrivial" surface that cannot be simplified. In non-mathematical terms, the surface of a suitcase is compressible, because we could cut the handle and shrink it into the surface. But a Conway sphere (a sphere with four holes) is incompressible, because there are essential parts of a knot or link both inside and out, so there is no way to move the entire knot or link to one side of the punctured sphere. The mathematical definition is as follows. There are two cases to consider. A sphere is incompressible if both inside and outside the sphere there are some obstructions that prevent the sphere from shrinking to a point and also prevent the sphere from expanding to enco (en)
- In geometria, e più precisamente in topologia, una superficie incompressibile è una superficie contenuta in una 3-varietà che non può essere "compressa" ad una superficie di genere minore. Questa proprietà può essere espressa efficacemente usando il gruppo fondamentale. Le superfici incompressibili sono importanti nello studio di una 3-varietà. Una 3-varietà irriducibile contenente una superficie incompressibile è detta di Haken: le soddisfano molte proprietà. (it)
- In de topologie, een deelgebied van de wiskunde, is een niet-samendrukbaar oppervlak, een oppervlak, dat is ingebed in een 3-variëteit, een oppervlak dat zo veel mogelijk kan worden vereenvoudigd, terwijl het binnen de 3-variëteit toch "niet-triviaal" blijft. Voor een precieze definitie, stel dat S een compact oppervlak is, dat op correcte wijze in een 3-variëteit M is ingebed. Stel verder dat D een schijf is, die is ook ingebed in M, met (nl)
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| - In der Mathematik sind inkompressible Flächen ein wichtiges Hilfsmittel der 3-dimensionalen Topologie. Durch Aufschneiden entlang inkompressibler Flächen können 3-dimensionale Mannigfaltigkeiten in einfachere Stücke zerlegt werden. (de)
- In mathematics, an incompressible surface is a surface properly embedded in a 3-manifold, which, in intuitive terms, is a "nontrivial" surface that cannot be simplified. In non-mathematical terms, the surface of a suitcase is compressible, because we could cut the handle and shrink it into the surface. But a Conway sphere (a sphere with four holes) is incompressible, because there are essential parts of a knot or link both inside and out, so there is no way to move the entire knot or link to one side of the punctured sphere. The mathematical definition is as follows. There are two cases to consider. A sphere is incompressible if both inside and outside the sphere there are some obstructions that prevent the sphere from shrinking to a point and also prevent the sphere from expanding to encompass all of space. A surface other than a sphere is incompressible if any disk with its boundary on the surface spans a disk in the surface. Incompressible surfaces are used for decomposition of Haken manifolds, in normal surface theory, and in the study of the fundamental groups of 3-manifolds. (en)
- In geometria, e più precisamente in topologia, una superficie incompressibile è una superficie contenuta in una 3-varietà che non può essere "compressa" ad una superficie di genere minore. Questa proprietà può essere espressa efficacemente usando il gruppo fondamentale. Le superfici incompressibili sono importanti nello studio di una 3-varietà. Una 3-varietà irriducibile contenente una superficie incompressibile è detta di Haken: le soddisfano molte proprietà. Benché il termine corretto in italiano sia incomprimibile, è invalso l'uso di incompressibile come traduzione del termine inglese incompressible surface. (it)
- In de topologie, een deelgebied van de wiskunde, is een niet-samendrukbaar oppervlak, een oppervlak, dat is ingebed in een 3-variëteit, een oppervlak dat zo veel mogelijk kan worden vereenvoudigd, terwijl het binnen de 3-variëteit toch "niet-triviaal" blijft. Voor een precieze definitie, stel dat S een compact oppervlak is, dat op correcte wijze in een 3-variëteit M is ingebed. Stel verder dat D een schijf is, die is ook ingebed in M, met Stel ten slotte dat de kromme in S geen schijf binnen S begrenst. Dan wordt D een samendrukbare schijf voor S genoemd en kunnen wij S ook een samendrukbaar oppervlak in M noemen. Indien een dergelijke schijf niet bestaat en S niet de is, dan noemen we S niet-samendrukbaar (of meetkundig niet-samendrukbaar). (nl)
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