Group actions, corks and exotic smoothings of R4

• 成果类型: Article
• 署名作者: Gompf, Robert E.
• 署名单位: University of Texas System; University of Texas Austin
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0819-8
• 发表日期: 2018
• 页码: 1131-1168
• 关键词: gauge-theory; DECOMPOSITION; TOPOLOGY

摘要

We provide the first information on diffeotopy groups of exotic smoothings of R-4: For each of uncountably many smoothings, there are uncountably many isotopy classes of self-diffeomorphisms. We realize these by various explicit group actions. There are also actions at infinity by non-finitely generated groups, for which no nontrivial element extends over the whole manifold. In contrast, every diffeomorphism of the end of the universal R4 extends. Our techniques apply to many other open 4-manifolds, and are related to cork theory. We show that under broad hypotheses, cork twisting is equivalent (up to blowups) to twisting on an exotic R-4, and give applications.