An ongoing geometry notebook
Zadachnik
I’m working through Delone and Zhitomirsky’s geometry problems—one problem, one construction, and one open question at a time.
New paper · Russian · Published preprint
Плоские модели систем со связностью: характеризация и препятствия
Flat models of systems with connection: characterization and obstructions
When can a model treat its components as independent without losing the relationships between them? This paper studies systems described by a principal bundle with connection: conditions for trivial transport around loops, curvature-based error estimates, and topological obstructions.
One distinction matters throughout: on a space with noncontractible loops, a flat connection can still have nontrivial holonomy.