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The $v_n$-periodic Goodwillie tower on wedges and cofibres
Homology, Homotopy and Applications ( IF 0.8 ) Pub Date : 2020-01-01 , DOI: 10.4310/hha.2020.v22.n1.a10
Lukas Brantner 1 , Gijs Heuts 2
Affiliation  

We introduce general methods to analyse the Goodwillie tower of the identity functor on a wedge $X \vee Y$ of spaces (using the Hilton-Milnor theorem) and on the cofibre $\mathrm{cof}(f)$ of a map $f: X \rightarrow Y$. We deduce some consequences for $v_n$-periodic homotopy groups: whereas the Goodwillie tower is finite and converges in periodic homotopy when evaluated on spheres (Arone-Mahowald), we show that neither of these statements remains true for wedges and Moore spaces.

中文翻译:

$v_n$-定期的Goodwillie 塔在楔子和co纤维上

我们介绍了一般方法来分析空间楔形 $X \vee Y$ 上(使用希尔顿-米尔诺定理)和映射 $\mathrm{cof}(f)$ 上的恒等函子的 Goodwillie 塔f: X \rightarrow Y$。我们推导出 $v_n$-周期性同伦群的一些结果:虽然 Goodwillie 塔是有限的,并且在对球体 (Arone-Mahowald) 进行评估时收敛于周期性同伦,但我们表明这些陈述对于楔形和摩尔空间都不是真的。
更新日期:2020-01-01
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