π: E → B — total space, fiber, connection, and holonomy
Base Space S¹
Total Space E (Torus)
Fiber S¹ at θ
E = total space, B = base, F = fiber, π: E→B projection. A section s: B→E lifts base to total space. Connection = horizontal lift. Curvature = failure of lifts to commute → holonomy.