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Diagram of an exhaust manifold from a Kia Rio. 1. manifold; 2. gasket; 3. nut; 4. heat shield; 5. heat shield bolt Ceramic-coated exhaust manifold on the side of a performance car. In automotive engineering, an exhaust manifold collects the exhaust gases from multiple cylinders into one pipe.
This turns out to be easier than the 3- or 4-dimensional case: the 3-dimensional case is the Thurston geometrisation conjecture, and the 4-dimensional case was solved by Michael Freedman (1982) in the topological case, [5] but is a very hard unsolved problem in the smooth case. In dimension 5, the smooth classification of simply connected ...
If the base manifold is an n-sphere , then by iterating this procedure over several vector bundles over one can plumb them together according to a tree [3] §8. If T {\displaystyle T} is a tree, we assign to each vertex a vector bundle ξ {\displaystyle \xi } over S n {\displaystyle S^{n}} and we plumb the corresponding disk bundles together if ...
Let be a smooth manifold; a (smooth) distribution assigns to any point a vector subspace in a smooth way. More precisely, consists of a collection {} of vector subspaces with the following property: Around any there exist a neighbourhood and a collection of vector fields, …, such that, for any point , span {(), …, ()} =.
Pages in category "Smooth manifolds" The following 19 pages are in this category, out of 19 total. ... This page was last edited on 4 February 2012, ...
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For manifolds of dimension at most 6, any piecewise linear (PL) structure can be smoothed in an essentially unique way, [2] so in particular the theory of 4 dimensional PL manifolds is much the same as the theory of 4 dimensional smooth manifolds. A major open problem in the theory of smooth 4-manifolds is to classify the simply connected ...