Hurwitz's Freeness Property
Pierre-Yves Gaillard
TL;DR
This paper proves that the groupoid formed by PSL(2,Z) acting on irrational real numbers via linear fractional transformations is free, revealing a fundamental structural property of this mathematical action.
Contribution
It establishes the freeness of the groupoid associated with PSL(2,Z) acting on irrationals, a novel result in the study of group actions and groupoids.
Findings
The groupoid is free when PSL(2,Z) acts on irrationals.
Provides a new understanding of the structure of this group action.
Supports further research into related groupoid properties.
Abstract
The groupoid attached to the action of PSL(2,Z) on the irrational reals by linear fractional transformations is free.
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Taxonomy
TopicsAdvanced Algebra and Logic