MathDB3 problems
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Conjecture on Busemann points of free two-step nilpotent groups
Free two-step nilpotent Busemann-point conjecture. The set of Busemann points of with respect to the standard generating set is countable.
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Conjecture on horoboundaries and Busemann-point orbits in virtually nilpotent groups
Horoboundary and Busemann-point conjecture.
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Tointon–Yadin conjecture on Busemann points of groups of polynomial growth
Tointon–Yadin conjecture. The horoboundary of every finitely generated group of polynomial growth should contain only countably many Busemann points.