[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 55 (1002ﾚｽ)
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474: 2021/06/20(日)09:00 ID:13yA71vw(1/2) AAS
ある意味、新論文の学部レベルの§2の説明で、状況が変化したのでしょう。
Woitのブログで、
anon says: March 6, 2021 at 6:51 pm
To be fair to Mochizuki, his manuscript has a section two for non-specialists like myself which shows he’s sincere in trying to get people to understand his ideas.
Initially it didn’t make sense to me and I was tempted to arrogantly dismiss it as gibberish; but after reading it a few more times its main points are becoming profoundly clearer: how apparent contradictions disappear in mathematics once the overall structure is restructured in some part, despite the total information content remaining the same.
Robertsも、自分の§2.3に関するブログで、
If Mochizuki’s writing was less circumlocutory (why do we need fancy notation for basic objects? and reminders of how they are built?), then it would be easier to grasp these apparently illustrative and enlightening examples.
§2は、§2.2までにdxの積分の扱いを説明し、§2.3で、dxにおける、端の貼り合わせて積分において、dxの帯の”端点”として、貼り合わせを、スケルトンで比喩している。
475: 2021/06/20(日)09:00 ID:13yA71vw(2/2) AAS
外部ﾘﾝｸ:thehighergeometer.wordpress.com
下のPedroコメントで、、
1)I think you are wrong in saying that, “as all points are identified, then any space collapses to one point also” precisely because the skeletal category of topological spaces also contains its morphisms.
→スケルトンの§2.3(i)は正しいと認めたが、§2.3(ii)とは比喩とコメント返。
2)Mochizuki’s example is correct in the sense that identifying objects (essentially all k-dimensional spaces —I know this is not so, but bear with me—) may perfectly limit the reasoning because the “quotient” category may have much less information (objects and maps) than the original one.
→圏の商も、圏の情報を失わないのでは、とコメント返。
外部ﾘﾝｸ[pdf]:www.kurims.kyoto-u.ac.jp
で、商（圏/圏の同値）の極限(dx)を得て積分するのがIU幾何のアイデアであり、商を使うのは、これは理論の前提。
圏の情報が失なわれないなら、ラベルは要らない、だけど。
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