伸缩函子指南
A guide to telescopic functors
摘要:
在20世纪80年代中期,Pete Bousfield和我对每个素数p和每个正整数n构造了从空间到谱的某些p-局部“伸缩”函子Phi_n。它们具有将同伦理论的色方法与无限环空间理论联系起来的显著性质:粗略地说,谱Phi_n(Z)捕获了空间Z的v_n周期同伦。最近有各种新的用途,这些函子,这表明他们有一个核心作用,发挥在计算周期现象。在这里,我提供了一个指南,他们的建设,表征,应用和计算。
英文摘要:
In the mid 1980's, Pete Bousfield and I constructed certain p--local `telescopic' functors Phi_n from spaces to spectra, for each prime p and each positive integer n. These have striking properties that relate the chromatic approach to homotopy theory to infinite loopspace theory: roughly put, the spectrum Phi_n(Z) captures the v_n periodic homotopy of a space Z. Recently there have been a variety of new uses of these functors, suggesting that they have a central role to play in calculations of periodic phenomena. Here I offer a guide to their construction, characterization, application, and computation.
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