Orientable manifold
Orientable manifold It has been suggested that this ... In mathematics, a manifold or space is orientable if and only if it is possible ... ordinary, flat sheet of paper is an orientable, two-dimensional manifold. If you draw the ... dimensional space which obeys Euclidean geometry is orientable for two-dimensional objects: it is possible ... such a two-dimensional manifold is non-orientable for any one-dimensional objects: that ...
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Non-orientable wormhole
Non-orientable wormhole It has been suggested that Alice ... section. (Discuss) In wormhole theory, a non-orientable wormhole is a wormhole connection that appears ... universe that includes one of these "non-orientable" connections does not allow a global definition ...
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Talk:Orientable manifold
Talk:Orientable manifold I think it should go in ... space-time manifold is believed to be orientable? Is this a matter of practicality, or ... An unorientable space-time would have an orientable double cover. Wouldn't that be the ...
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Talk:Non-orientable wormhole
Talk:Non-orientable wormhole Merging Alice universe Alice universe is ...
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Orientability
... Orientability of surfaces The torus is an orientable surface. The Möbius strip is a non-orientable surface. Intuitively, a surface S in the Euclidean space R 3 is non-orientable, if a figure such as the figure ... within a plane). Otherwise the surface is orientable. More precisely (and applicable to non-embedded ... reflection map, then the surface is non-orientable. An abstract surface (i.e., a ...
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Lickorish–Wallace theorem
... of 3-manifolds states that any closed, orientable, connected 3-manifold may be obtained by ... Lickorish twist theorem , which states that any orientable automorphism of a closed orientable surface is generated by Dehn twists along ... of the theorem is that every closed, orientable 3-manifold bounds a simply-connected compact ... using his work on automorphisms of non-orientable surfaces, Lickorish also showed that every ...
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Genus (mathematics)
... few different, but closely related, meanings: Topology Orientable surface The genus of a connected, orientable surface is an integer representing the maximum ... a coffee mug with a handle. Non-orientable surface The (non-orientable) genus of a connected, non-orientable closed surface is a positive integer ...
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Haken manifold
... sided incompressible surface. Sometimes one considers only orientable Haken manifolds, in which case a Haken manifold is a compact, orientable, irreducible 3-manifold that contains an orientable, incompressible surface. A 3-manifold finitely covered ... We will consider only the case of orientable Haken manifolds, as this simplifies the discussion; a regular neighborhood of an orientable surface in an orientable 3-manifold ...
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Connected sum   (translated from German)
... theorem of Helmut Kneser (1930): Each compact, orientable 3-Mannigfaltigkeit is the connected sum of ... 2 \times S^1, the non-orientable $S^2$Bundle over orientable 3-Mannigfaltigkeit is < the connected sum a ... collection of irreducible 3-Mannigfaltigkeiten and non-orientable;math>S^2Bundles over < ...
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Prime decomposition (3-manifold)
... for 3-manifolds states that every compact, orientable 3-manifold is the connected sum of ... times S^1 or the non-orientable $S^2$ bundle over orientable 3-manifold is a connected sum of irreducible 3-manifolds and non-orientable $S^2$ bundles over < ...
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