主 讲 人 ：杨聚鑫    

活动时间：2025-12-19 16:10:00

地      点 ：数学科学学院D203报告厅

主办单位：数学科学学院

讲座内容：

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 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 2-torsion parts of the unstable homotopy groups \pi_{i}(\Sigma(S^{n} \cup e^{n+k+1})), where 3n + 2k + 1 < i <4n + 3k + 3 and n>1, provided the requisite homotopy groups of spheres are known.

The proof requires the Hopf algbra structure of the looped homotopy fibre of the pinch map, giving a generalization of a result of    Cohen-Moore-Neisendorfer’s 1979 classic  paper.

主讲人介绍：

杨聚鑫，大连理工大学博士生。2023年从河北师范大学硕士研究生毕业，导师是吴杰教授。2021年4月-2025年8月在北京雁栖湖应用数学研究院访问、实习。研究兴趣为非稳定同伦群的计算、Toda bracket 理论以及回路空间的同伦分解的表示伦方法。其成果发表在 Algebr. Geom. Topol. , Homology Homotopy and Applications, Topology and its Applications 等。