  The study of the propagation of electrons with a varying spinor orientability
is performed using the coordinate transformation method. Topological Insulators
are characterized by an odd number of changes of the orientability in the
Brillouin zone. For defects the change in orientability takes place for closed
orbits in real space. Both cases are characterized by nontrivial spin
connections. Using this method , we derive the form of the spin connections for
topological defects in three dimensional Topological Insulators. On the surface
of a Topological Insulator, the presence an edge dislocation gives rise to a
spin connection controlled by torsion. We find that electrons propagate along
two dimensional regions and confined circular contours. We compute for the edge
dislocations the tunneling density of states. The edge dislocations violates
parity symmetry resulting in a current measured by the in-plane component of
the spin on the surface.
