Year: 2022
Type: preprint
Abstract: Let $p$ be a prime and let $π^n(X;\mathbb{Z}/p^r)=[X,M_n(\mathbb{Z}/p^r)]$ be the set of homotopy classes of based maps from CW-complexes $X$ into the mod $p^r$ Moore spaces $M_n(\mathbb{Z}/p^r)$ of degree $n$, where $\mathbb{Z}/p^r$ denotes the integers mod $p^r$. In this paper we firstly determine the modular cohomotopy groups $π^n(X;\mathbb{Z}/p^r)$ up to extensions by classical methods of primary cohomology operations and give conditions for the splitness of the extensions. Secondly we utilize some unstable homotopy theory of Moore spaces to study the modular cohomotopy groups; especially, the group $π^3(X;\mathbb{Z}_{(2)})$ with $\dim(X)\leq 6$ is determined.
Source: arXiv (Cornell University)
Authors: Li, Pengcheng, Pan, Jianzhong, Wu, Jie
Institution: Southern University of Science and Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4286743991