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

学术报告

拓扑研讨班

Speaker:  杨聚鑫 （大连理工大学）

Inviter: 黄瑞芝

Language: Chinese

Title: A “Periodicity” phenomenon of the attaching map of the 2-cell  complexes

Time & Venue: 2026年1月12日（星期一） 14: 30-15: 30 & N933

Abstract:  In this talk, I would like to introduce our recent work on the “Periodicity” phenomenon of the attaching map of the suspended two-cell CW complex. I will first introduce Selick-Wu's A^{min}-theory, a theory on the homotopy functor decomposition and becoming a bridge between homotopy theory and the representation theory. Employing this theory, we deduce that the attaching map of the CW complex above manifests a“periodicity”phenomenon. The result essentially furnishes, up to the present, one of the most effective methods for computing the unstable homotopy groups of 2-cell complexes in the J_{4}-range.

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Title: Introduction to the classical methods for computing the unstable homotopy groups

Time & Venue: 2026年1月12日（星期一） 15: 30-16: 30 & N933

Abstract: In this talk, we review classical Toda-style methods for computing unstable homotopy groups of spheres, 2-cell complexes, and SO(n), and present recent progress based on these techniques.