
TL;DR
This paper develops a homotopy theory for global actions, algebraic structures analogous to topological spaces, and establishes a Galois correspondence between their coverings and fundamental groups.
Contribution
It introduces the homotopy theory of global actions and proves a Galois correspondence linking coverings to subgroups of the fundamental group.
Findings
Established a Galois correspondence for global actions
Connected coverings correspond to subgroups of the fundamental group
Developed foundational homotopy theory for global actions
Abstract
A global action is an algebraic analogue of a topological space. It consists of group actions , , which fulfill a certain compatibility condition. We investigate the homotopy theory of global actions. The main result establishes a Galois type correspondence between connected coverings of a given connected global action and subgroups of the fundamental group of that action.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory · Algebraic Geometry and Number Theory
