  In this article we use a geometric approach to study geometric phases in
graphitic cones. The spinor that describes the low energy states near the Fermi
energy acquires a phase when transported around the apex of the cone, as found
by a holonomy transformation. This topological result can be viewed as an
analogue of the Aharonov-Bohm effect. The topological analysis is extended to a
system with $n$ cones, whose resulting configuration is described by an
effective defect.
