INFINITARY COMMUTATIVITY AND ABELIANIZATION IN FUNDAMENTAL GROUPS

Author:

BRAZAS JEREMYORCID,GILLESPIE PATRICK

Abstract

Abstract Infinite product operations are at the forefront of the study of homotopy groups of Peano continua and other locally path-connected spaces. In this paper, we define what it means for a space X to have infinitely commutative $\pi _1$ -operations at a point $x\in X$ . Using a characterization in terms of the Specker group, we identify several natural situations in which this property arises. Maintaining a topological viewpoint, we define the transfinite abelianization of a fundamental group at any set of points $A\subseteq X$ in a way that refines and extends previous work on the subject.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The Griffiths double cone group is isomorphic to the triple;Pacific Journal of Mathematics;2023-12-31

2. Fundamental groups of James reduced products;Topology and its Applications;2022-08

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