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arXiv · 2609.27820

Bergman's amalgamation problem over the circle

Andreas Thom
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Abstract

We prove that $S^1$, ${\rm SU}(2)$, and ${\rm SO}(3)$ are compact amalgamation bases: for each of these groups, any two compact groups with specified embedded copies of it embed in a compact group in which those copies agree. For compact Lie groups, the amalgam can be chosen to be a finite-dimensional unitary group. This research was conducted with substantial AI assistance, including in the development of mathematical constructions and proof arguments.

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Andreas Thom. 2026-09-23. Bergman's amalgamation problem over the circle. https://arxiv.org/abs/2609.27820

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