中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
拓扑研讨班
Speaker: 胥夫鹏（中国科学院数学与系统科学研究院）
Inviter: 苏阳
Language: Chinese
Title: On the simplest simply connected non-spin rational homology 7-spheres that are not 2-connected
Time & Venue: 2026年3月23日（星期一）14：30-15：30 & N820
Abstract:Rational homology spheres occupy a distinguished position in topology, encoding torsion phenomena. In low dimensions they already play an important role, and in higher dimensions they provide a testing ground for surgery theory and manifold classification. For simply connected cases, the classification is well understood in dimensions five and six, whereas dimension seven exhibits much richer topology. This is reflected in Milnor's λ-invariant, originally defined for homotopy 7-spheres, detecting exotic smooth structures on the 7-sphere and extending to all rational homology 7-spheres. In this talk, we classify the simplest non-spin non-2-connected cases, showing that these manifolds are completely determined by the λ-invariant.
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