منابع مشابه
Combinatorial Embeddings of Manifolds
The following results on embedding manifolds resemble in their form Dehn's Lemma, the Sphere Theorem, and, especially, embedding theorems obtained for differentiable manifolds by A. Haefliger [i]. Let M, Q be finite combinatorial manifolds of dimensions m and q, respectively. Let M, Q be their boundaries (possibly empty), and let ƒ : M—>Q be a piecewise linear map. We define sing (ƒ) to be the ...
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We prove that a (2m n+1)-connectedmap f : Mm ! Xn from a compact PL m-manifoldM to a generalized n-manifoldX with the disjoint disks property, 3m 2n 2, is homotopic to a tame embedding. There is also a controlled version of this result, as well as a version for noncompactM and proper maps f that are properly (2m n+ 1)-connected. The techniques developed lead to a general position result for arb...
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We study a version of Whitney’s embedding problem in projective geometry: What is the smallest dimension of an affine space that can contain an n-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points? This problem is related to the generalized vector field problem, existence of non-singular bilinear maps, and the immersion problem for real projec...
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The dot in (1) denotes the usual scalar product of R. The notion embedding means, that w is locally an immersion and globally a homeomorphism of M onto the subspace u(M) of R*. If an embedding w : M -• R satisfies (1) on the whole M, we speak of an isometric embedding. If w is an immersion and a solution of (1) in a (possibly small) neighbourhood of any point of M, we speak of a local isometric...
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We consider existence and uniqueness of two kinds of coisotropic embeddings and deduce the existence of deformation quantizations of certain Poisson algebras of basic functions. First we show that any submanifold of a Poisson manifold satisfying a certain constant rank condition, already considered by Calvo and Falceto (2004), sits coisotropically inside some larger cosymplectic submanifold, wh...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1962
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1962-10684-3