PreprintCC BY 4.0arXiv
Bergman's amalgamation problem over the circle
Abstract
We prove that S1, SU(2), and 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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BibTeX
@misc{thom2026bergmans,
title = {{Bergman's amalgamation problem over the circle}},
author = {Andreas Thom},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27820},
eprint = {2609.27820},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27820},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bergman's amalgamation problem over the circle
AU - Andreas Thom
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.27820
UR - https://arxiv.org/abs/2609.27820
AB - We prove that S^1, SU(2), and 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.
ER -