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
代数拓扑研讨班
Speaker: Yuchen Wu (UCSD)
Inviter: 邹佛灵
Language: Chinese
Title: A cofiber-of-$ au$ approach to hidden extensions and equivariant slice differentials
Time & Venue: 2026年6月15日（星期一）10：00-11：00 & zoomID:851 4508 8872
Abstract: Lin--Wang--Xu's resolution of the last open case of the Kervaire invariant problem is a landmark achievement in recent Adams spectral sequence computations, powered by new principles for organizing hidden extensions and splicing differentials. The cofiber-of-$ au$ formalism allows these principles to be realized in a much broader setting. In this talk, I will use this perspective to extend the generalized Leibniz rule and the generalized Mahowald trick of Lin--Wang--Xu from Adams spectral sequences to all spectral sequences arising from filtered spectra.
These methods are then applied to equivariant slice spectral sequences for the Hill--Hopkins--Ravenel theories $BP^{((C_4))}langle m angle$, producing new families of exotic transfer differentials for every $m$. The talk will also discuss a layered notion of extension, which refines the usual notion of hidden extension by recording the filtration at which the extension is witnessed. This refinement is natural in the setting of filtered spectra, and gives a slightly sharper form of the Lin--Wang--Xu methods even when specialized back to Adams spectral sequences.
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