On visualisation of completions of free groups
Yury A. Neretin
TL;DR
This paper explores visualizing the pronilpotent completion of finitely generated free groups as subgroups within free Lie groups, providing a geometric perspective on algebraic structures.
Contribution
It introduces a method to represent the pronilpotent completion of free groups as subgroups in free Lie groups, offering new insights into their structure.
Findings
Established a correspondence between free group completions and Lie groups
Provided a visualization framework for algebraic completions
Enhanced understanding of free group structures
Abstract
Our purpose is to visualize the pronilpotent completion of a finitely generated free group as a certain subgroup in the free Lie group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology