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(Co)homology self-closeness numbers of simply-connected spaces
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2021-01-01 , DOI: 10.4310/hha.2021.v23.n1.a1
Pengcheng Li 1
Affiliation  

The (co)homology self-closeness number of a simply-connected based CW-complexes $X$ is the minimal number $k$ such that any self-map $f$ of $X$ inducing an automorphism of the (co)homology groups for dimensions$\leq k$ is a self-homotopy equivalence. These two numbers are homotopy invariants and have a close relation with the group of self-homotopy equivalences. In this paper, we compare the (co)homology self-closeness numbers of spaces in certain cofibrations, define the mod $p$ (co)homology self-closeness number of simply-connected $p$-local spaces with finitely generated homologies and study some properties of the (mod $p$) (co)homology self-closeness numbers.

中文翻译:

单连通空间的(共)同调自近度数

基于简单连接的 CW 复合体 $X$ 的 (co)homology self-closeness number 是最小数 $k$,使得 $X$ 的任何自映射 $f$ 导致 (co)homology 的自同构维度$\leq k$ 的组是一个自同伦等价。这两个数是同伦不变量,与自同伦等价群有密切关系。在本文中,我们比较了某些共纤维中空间的(共)同调自接近数,定义了具有有限生成同调的简单连接$p$-局部空间的模$p$(共)同调自接近数,以及研究 (mod $p$) (co)homology self-closeness number 的一些性质。
更新日期:2021-01-01
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