mapping torus造句

例句与造句

1. In short, an open book is a mapping torus with solid tori glued in so that the core circle of each torus runs parallel to the boundary of the fiber.
2. Compact manifolds with this geometry include the mapping torus of a Dehn twist of a 2-torus, or the quotient of the Heisenberg group by the " integral Heisenberg group ".
3. For an appropriate choice of almost complex structure, punctured holomorphic curves ( of finite energy ) in it have cylindrical ends asymptotic to the loops in the mapping torus corresponding to fixed points of the symplectomorphism.
4. For instance, in symplectic Floer homology, one considers the product of the mapping torus of a symplectomorphism with the real numbers; in symplectic field theory, one considers the symplectization of a contact manifold.
5. The first two cases are comparatively easy, while the existence of a hyperbolic structure on the mapping torus of a pseudo-Anosov homeomorphism is a deep and difficult theorem ( also due to sphere-filling curve.
6. It's difficult to find mapping torus in a sentence. 用mapping torus造句挺难的
7. SFH is the homology of the chain complex generated by the fixed points of such a symplectomorphism, where the differential counts certain pseudoholomorphic curves in the product of the real line and the mapping torus of the symplectomorphism.
8. When ? is an oriented compact surface with " n " boundary components and ? : ? ?! ? is a homeomorphism which is the identity near the boundary, we can construct an open book by first forming the mapping torus ? ?.
9. For example, the mapping torus of an Anosov map of a torus has a finite volume sol structure, but its JSJ decomposition cuts it open along one torus to produce a product of a torus and a unit interval, and the interior of this has no finite volume geometric structure.
10. Examples of applications of train tracks include : a theorem of Brinkmann proving that for an automorphism " ? " of " F n " the mapping torus group of " ? " is isoperimetric inequality; a proof of algorithmic solvability of the conjugacy problem for free-by-cyclic groups; and others.
11. It can be used to describe the structure of the set of fiberings of M over the circle : if M can be written as the mapping torus of a diffeomorphism f of a surface S then the embedding S \ hookrightarrow M represents a class in a top-dimensional ( or open ) face of B : moreover all other integer points on the same face are also fibers in such a fibration.
12. There is a unique minimal way of cutting an irreducible oriented 3-manifold along tori into pieces that are Seifert manifolds or atoroidal called the JSJ decomposition, which is not quite the same as the decomposition in the geometrization conjecture, because some of the pieces in the JSJ decomposition might not have finite volume geometric structures . ( For example, the mapping torus of an Anosov map of a torus has a finite volume solv structure, but its JSJ decomposition cuts it open along one torus to produce a product of a torus and a unit interval, and the interior of this has no finite volume geometric structure .)