Highly connected 7-manifolds and non-negative sectional curvature

• 成果类型: Article
• 署名作者: Goette, S.; Kerin, M.; Shankar, K.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2020.191.3.3
• 发表日期: 2020
• 页码: 829-892
• 关键词: equivariant eta-invariants; exotic spheres; CLASSIFICATION; MANIFOLDS; biquotients; s-3-bundles; COHOMOLOGY

摘要

In this article, a six-parameter family of highly connected 7-manifolds which admit an SO(3)-invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an SO(3)-invariant metric of non-negative curvature.