Transversality for piecewise linear manifolds
نویسندگان
چکیده
منابع مشابه
Piecewise Linear Transversality
We prove transversality theorems for piecewise linear manifolds, maps and polyhedra. Our main result is that given two closed manifolds contained in a third, then one can be ambient isotoped until it is transversal to the other. This result is then extended to maps and polyhedra. The transversality theory for smooth manifolds was initiated by Thorn in his classical paper [8], and has been exten...
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Transversality phenomena are studied for homology manifolds. For homology manifolds X, Y and Z, with Z embedded in Y with a neighborhood ν(Z) which has a given bundle structure, we define a map f : X → Y to be transverse to Z, if f−1(Z) = Z′ is a homology manifold, the neighborhood f−1(ν(Z)) has a bundle structure given by f∗ν(Z) and f induces the bundle map. In the case where the range is a ma...
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In this thesis we introduce a ∆-set Ψ d (R )• which we regard as the piecewise linear analogue of the space Ψd(R ) of smooth d-dimensional submanifolds in R introduced by Galatius in [4]. Using Ψ d (R )• we define a bi-∆-set Cd(R )•,• whose geometric realization BC d (R ) = ∥∥Cd(RN )•,•∥∥ should be interpreted as the PL version of the classifying space of the category of smooth d-dimensional co...
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In this thesis we introduce a ∆-set Ψ d (R )• which we regard as the piecewise linear analogue of the space Ψd(R ) of smooth d-dimensional submanifolds in R introduced by Galatius in [4]. Using Ψ d (R )• we define a bi-∆-set Cd(R )•,• whose geometric realization BC d (R ) = ∥∥Cd(RN )•,•∥∥ should be interpreted as the PL version of the classifying space of the category of smooth d-dimensional co...
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Suppose that X is a generalized n-manifold, n 5, satisfying the disjoint disks property, and M and Q are topologicalmand q-manifolds, respectively, 1-LCC embedded in X, with n m 3 and n q 3. We de ne what it means for M to be stably transverse to Q in X. In the metastable range, 3m 2(n 1) and 3(m+ q) < 4(n 1), we show that there is an arbitrarily small homotopy of M to a 1-LCC embedding that is...
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ژورنال
عنوان ژورنال: Topology
سال: 1967
ISSN: 0040-9383
DOI: 10.1016/0040-9383(67)90003-1