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Constructions of self-maps of $\operatorname{SU}(4)$ via Postnikov towers
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2020-05-20 , DOI: 10.4310/hha.2020.v22.n2.a23
Jim Fowler 1 , Chris Kennedy 1
Affiliation  

Cohomology operations restrict the degree of a self-map of $\operatorname{SU}(4)$ to be either odd or a multiple of $8$; we find self-maps realizing these possible degrees. The notion of the degree of a self-map can be refined to a notion of multidegree which records the effect of the self-map on each of the generators of $H^{\star} (\operatorname{SU}(4))$. We find restrictions on the possible multidegrees of self-maps of $\operatorname{SU}(4)$ and, via Postnikov towers, build self-maps stage-by-stage realizing the possible multidegrees.

中文翻译:

通过Postnikov塔构建$ \ operatorname {SU}(4)$的自映射

同上运算将$ \ operatorname {SU}(4)$的自映射的程度限制为$ 8 $的奇数或倍数;我们发现实现这些可能程度的自映射。自图度的概念可以细化到的概念multidegree它记录每个$ H ^ {\星}的发电机的自贴图的效果(\ operatorname {SU}(4)) $。我们发现对$ \ operatorname {SU}(4)$的可能多度数自映射的限制,并通过Postnikov塔,逐步构建自映射,以实现可能的多度数。
更新日期:2020-07-20
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