Geometry and Topology Seminar —— Transfer maps of profinite groups and their application in chromatic homotopy theory
报告人：李谷川（国产自慰
）
时间：2025-10-15 15:10-17:00
地点：智华楼四元厅（225）
【摘要】
For a fintie cover of spaces from E to B, there is a "wrong way map", the transfer map, from the cohomology of E to the cohomology of B. This agrees with the transfer map in group cohomology. We will define a similar transfer map for a profinite group with finite cohomology dimension. As an application, after K(1)-localization, the classical J-homomorphism can be interpreted as a profinite transfer map. In joint work in progress with Ningchuan Zhang, we extend this idea to define and study profinite transfers between homotopy fixed points of the Morava E-theory for closed subgroups of the Morava stabilizer group. This defines analogs of the J-homomorphism at higher chromatic heights.
