In
mathematics, specifically in
differential topology, a Kervaire manifold
is a
piecewise-linear manifold of
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coor ...
constructed by by plumbing together the
tangent bundle
In differential geometry, the tangent bundle of a differentiable manifold M is a manifold TM which assembles all the tangent vectors in M . As a set, it is given by the disjoint unionThe disjoint union ensures that for any two points and of ...
s of two
-spheres, and then gluing a
ball to the result. In 10 dimensions this gives a piecewise-linear manifold with no
smooth structure In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows one to perform mathematical analysis on the manifold.
Definition
A smooth structure on a manifold M is ...
.
See also
*
Exotic sphere
References
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Differential topology
Manifolds
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