题 目：A generalization of the Atiyah-Segal completion theorem for the equivariant Real K-theory

报告人：林兆波教授 (Hong Kong)

Abstract: The first instance of the completion theorem was due to Atiyah and Hirzebruch. It was a result about the (complex) K-theory of the classifying spaces of compact connected Lie groups. Atiyah later proved the result for the finite groups. In these two cases, the statements were about the inverse limits of the K-groups of the finite subcomplexes of the classifying spaces. In late 60s, using the idea due to Grothendieck of pro-group valued cohomology theory, Atiyah and Segal were able to prove a completion theorem for compact (not necessarily connected) Lie groups and the statement was about the genuine K-theory of the (infinite complexes of) the classifying spaces of the compact Lie groups rather than the inverse limits. The proof was sufficiently natural that the case for compact Real Lie groups also went through. In the 80s, four topologists (Adams, Haeberly, Jackowski and May) were able to prove a generalization of the completion theorem for equivariant complex K-theory. They proceeded by induction on the dimensions of the compact Lie groups. While their proof was sufficiently natural that it worked also for real K-theory (note the difference between real and Real), they were unable to prove the result for Real K-theory. In this talk, we give a proof of the generalization of the completion theorem for the equivariant Real K-theory.

时间： 3月1日（周五）下午2:00开始

地点：565net必赢客户端本部教二楼627教室

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