23/12/20 13:26:58.30 pnzIsqbw.net
>>678-680
別に逆らうわけではないので
事実として淡々と見てもらえればうれしい
下記、Cobordism en.wikipedia にあるように、二つのn次元多様体 MとNに対して、それを一次元高いn+1次元空間に埋め込んで
それをn+1次元多様体Wでつなぐ。（図があるので、見てください）
（>>676 松本幸夫 著 · 2019 — Thom の 'コボルディズム理論' これは，'同境 (cobordant)'. というごく粗い同値関係により，すべての次元のすべての閉じた多様体を分類し なども）
よって、双対ではなく、同値関係ですね
なお
”The theory was originally developed by René Thom for smooth manifolds (i.e., differentiable), but・・”
とあるので、ルネ・トムの創案だろう（下記だね。私の記憶とも合っている）
”グロタンディークとの不仲でも知られる”とあるように、
晩年はトポロジー いや 数学から 離れたらしい（G氏との不仲も一因らしい）
接尾辞 -ism については、下記ご参照
(参考)
URLﾘﾝｸ(en.wikipedia.org)
Cobordism
Two manifolds of the same dimension are cobordant if their disjoint union is the boundary of a compact manifold one dimension higher.
A cobordism (W; M, N). URLﾘﾝｸ(upload.wikimedia.org)
The boundary of an (n + 1)-dimensional manifold W is an n-dimensional manifold ∂W that is closed, i.e., with empty boundary. In general, a closed manifold need not be a boundary: cobordism theory is the study of the difference between all closed manifolds and those that are boundaries.
The theory was originally developed by René Thom for smooth manifolds (i.e., differentiable), but there are now also versions for piecewise linear and topological manifolds.
A cobordism between manifolds M and N is a compact manifold W whose boundary is the disjoint union of M and N,
∂W=M ∪ N.
Definition
Manifolds
The terminology is usually abbreviated to (W;M,N)}.[1]
M and N are called cobordant if such a cobordism exists.
All manifolds cobordant to a fixed given manifold M form the cobordism class of M.
つづく