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math.DG2026
A kinematic explanation of the 1:3 ratio for rolling spheres and the exceptional simple Lie group of rank two
Jacob W. Erickson
Given a pair of (round) 2-dimensional spheres, one of which has radius three times that of the other, the Lie algebra of local infinitesimal symmetries for the distribution corresp…
math.DG2026
Inequivalence of the various notions of completeness for Cartan geometries
Jacob W. Erickson, Benjamin McKay
We demonstrate that the three prevailing notions of completeness for Cartan geometries are not actually equivalent and provide methods for constructing many examples in the affine…