Hirsch M., Mazur B. — Smoothings of Piecewise Linear Manifolds. (AM-80) (Annals of Mathematics Studies)
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Название: Smoothings of Piecewise Linear Manifolds. (AM-80) (Annals of Mathematics Studies)
Авторы: Hirsch M., Mazur B.
Аннотация:
The triangulation theorems of Whitehead [12] show that to every smooth manifold V there is associated a PL manifold M and a homeomorphism
f:M -, V, having particularly nice local properties. Moreover M and f
are unique .up to very strong equivalence relations. When M is triangu-
lated, f is called a smooth triangulation of V.
Whitehead's results suggest the inverse problem: is a given combina-
torial manifold M the domain of a smooth triangulation of some smooth
manifold V? This is possible if and only if M has a smootblng, i.e., a
differential structure which is compatible with its piecewise linear struc-
ture.
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