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談話会・数理科学講演会
過去の記録 ～04/23｜次回の予定｜今後の予定 04/24～
| 担当者 | 足助太郎，寺田至，長谷川立，宮本安人（委員長） |
|---|---|
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index.html |
2006年06月23日(金)
17:00-18:00 数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:30～17:00(コモンルーム)
Robert Gompf 氏 (University of Texas at Austin)
25 years of exotic $\\mathbb{R}^4s$
お茶&Coffee&お菓子: 16:30～17:00(コモンルーム)
Robert Gompf 氏 (University of Texas at Austin)
25 years of exotic $\\mathbb{R}^4s$
[ 講演概要 ]
A quarter century ago, 4-manifold theory was revolutionized by the Fields-Medal winning breakthroughs of Freedman and Donaldson, with Freedman showing that topological 4-manifolds behave like their higher dimensional counterparts, but Donaldson showing that smooth 4-manifolds behave in a completely different way. The interplay between these theories produces results unique to dimension 4: A fixed topological 4-manifold often admits infinitely many distinct smooth structures, for which no classification scheme is yet available. The quintessential example is that in contrast with other dimensions, Euclidean 4-space admits exotic smooth structures. That is, there are "exotic R^4s" homeomorphic to R4 but not diffeomorphic to it. We will survey what has been learned about these strange creatures in the last quarter century, and exhibit an explicit example.
A quarter century ago, 4-manifold theory was revolutionized by the Fields-Medal winning breakthroughs of Freedman and Donaldson, with Freedman showing that topological 4-manifolds behave like their higher dimensional counterparts, but Donaldson showing that smooth 4-manifolds behave in a completely different way. The interplay between these theories produces results unique to dimension 4: A fixed topological 4-manifold often admits infinitely many distinct smooth structures, for which no classification scheme is yet available. The quintessential example is that in contrast with other dimensions, Euclidean 4-space admits exotic smooth structures. That is, there are "exotic R^4s" homeomorphic to R4 but not diffeomorphic to it. We will survey what has been learned about these strange creatures in the last quarter century, and exhibit an explicit example.
