A “piecewise-linear” method for triangulating 3-manifolds
نویسندگان
چکیده
منابع مشابه
Invariants of Piecewise - Linear 3 - Manifolds
The purpose of this paper is to present an algebraic framework for constructing invariants of closed oriented 3-manifolds. The construction is in the spirit of topological field theory and the invariant is calculated from a triangulation of the 3-manifold. The data for the construction of the invariant is a tensor category with a condition on the duals, which we have called a spherical category...
متن کاملSpaces of Piecewise Linear Manifolds
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...
متن کاملSpaces of Piecewise Linear Manifolds
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...
متن کاملTriangulating 3-manifolds Using 5 Vertex Link Types
WE SHOW that a closed orientable 3-manifold can be triangulated in a simple way locally. There are 5 triangulations of S2 with the property that every such manifold has a triangulation in which the link of each vertex is one of these 5 link types. This triangulation is obtained from a paving of the manifold by cubes. In this paving, the order of every edge is 3,4 or 5. Denoting the union of the...
متن کاملSectional Curvature in Piecewise Linear Manifolds
A metric complex M is a connected, locally-finite simplicial complex linearly embedded in some Euclidean space R. Metric complexes M and M' are isometric if they have subdivisions L and L and if there is a simplicial isomorphism h:L -• L such that for every a e L, the linear map determined by h\a -• h(a) is an isometry (that is, it extends to an isometry of the affine spaces generated by these ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1984
ISSN: 0001-8708
DOI: 10.1016/0001-8708(84)90050-1