smoothable การใช้

• So Freedman's classification implies there are many non-smoothable 4-manifolds, for example the E8 manifold.
• However, while a smooth manifold is not a PL manifold, it carries a canonical PL structure  it is uniquely triangularizable; conversely, not every PL manifold is smoothable.
• Pontryagin numbers can also be defined for PL manifolds, and Milnor showed that his PL manifold had a non-integral value of " p " 2, and so was not smoothable.
• The existence of non-smoothable manifolds was proven by, see Kervaire manifold, and later explained in the context of Donaldson's theorem ( compare Hilbert's fifth problem ); a good example of a non-smoothable manifold is the E 8 manifold.
• The existence of non-smoothable manifolds was proven by, see Kervaire manifold, and later explained in the context of Donaldson's theorem ( compare Hilbert's fifth problem ); a good example of a non-smoothable manifold is the E 8 manifold.