3 papers
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…
math.DG2025
A method for determining Cartan geometries from the local behavior of automorphisms
Jacob W. Erickson
We introduce a construction for a Cartan geometry that captures the local behavior of a given geometric automorphism near a distinguished element. The result of this construction,…
math.DG2025
Holonomy of parabolic geometries near isolated higher-order fixed points
Jacob W. Erickson
For Cartan geometries admitting automorphisms with isotropies satisfying a particular, loosely dynamical property on their model geometries, we demonstrate the existence of an open…