>>745
>>手持ちの「4次元多様体 I&II 上正明・松本 幸夫(著) 2022年02月版」を調べるべきだし
>その本にはノビコフの定理の証明はもちろん、ステートメントも書いてない
>要するに、そこはもう松本幸夫氏の「４次元のトポロジー」に書かれてる通りだから

ちがう！
・えーと>>739より再録
(参考)
https://en.wikipedia.org/wiki/Classification_of_manifolds
Classification of manifolds

Dimension 4: exotic
Further information: 4-manifold
Four-dimensional manifolds are the most unusual: they are not geometrizable (as in lower dimensions), and surgery works topologically, but not differentiably.

Since topologically, 4-manifolds are classified by surgery, the differentiable classification question is phrased in terms of "differentiable structures": "which (topological) 4-manifolds admit a differentiable structure, and on those that do, how many differentiable structures are there?"

Four-manifolds often admit many unusual differentiable structures, most strikingly the uncountably infinitely many exotic differentiable structures on R4. Similarly, differentiable 4-manifolds is the only remaining open case of the generalized Poincaré conjecture.

Dimension 5 and more: surgery
Further information: surgery theory
In dimension 5 and above (and 4 dimensions topologically), manifolds are classified by surgery theory.

The reason for dimension 5 is that the Whitney trick works in the middle dimension in dimension 5 and more: two Whitney disks generically don't intersect in dimension 5 and above,by general position (2+2<5).
In dimension 4, one can resolve intersections of two Whitney disks via Casson handles, which works topologically but not differentiably; see Geometric topology: Dimension for details on dimension.
(引用終り)

・上記に書いてあることは、”In dimension 5 and above (and 4 dimensions topologically), manifolds are classified by surgery theory.”
　要するに、5次元以上では ”two Whitney disks”が交差（intersect）しない関係で、surgery theoryが使える
　4次元では、”one can resolve intersections of two Whitney disks via Casson handles”
　つまり、Whitney diskの代わりにCasson handleが使えるので、”topologically but not differentiably”で、5次元以上と同じことができると
・Casson handle https://en.wikipedia.org/wiki/Casson_handle
　を見てください

つづく