Bergman's amalgamation problem over the circle
Andreas Thom
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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