AI 中文总结
研究利用新型操作代数，从轨道预层上的函子构造 \(G\)-谱，给出麦基函子新描述，定义拓扑麦基函子并构造相关 \(G\)-谱，还引出多种 \(G\)-谱，虽引发诸多问题，但有重要理论意义。
AI 中文摘要
设 \(G\) 为有限群。利用一种新型操作代数，我们对公理化并探索了一种无穷循环空间机器，该机器从轨道预层上结构适当的函子构造（真正的）\(G\)-谱，轨道预层是从 \(G\) 的轨道范畴到带基点空间的反变函子。该理论意外地引出了麦基函子的新操作代数描述，进而定义了“拓扑麦基函子”并构造了其相关的 \(G\)-谱。还引出了皮卡 \(G\)-谱、阿祖马亚环 \(G\)-谱和布劳尔 \(G\)-谱。这些构造引发了许多未解决的问题。
英文摘要
Let $G$ be a finite group. Using a new kind of operad, we axiomatize and explore an infinite loop space machine that constructs (genuine) $G$-spectra from suitably structured functors on orbital presheaves, which are just contravariant functors from the orbit category of $G$ to based spaces. The theory leads unexpectedly to a new operadic description of Mackey functors and hence to a definition of ``topological Mackey functors" and a construction of their associated $G$-spectra. It also leads to Picard $G$-spectra, Azumaya ring $G$-spectra, and Brauer $G$-spectra. These constructions raise many unanswered questions.
Comments50 pages
