  It is well known that a Bosonic Mott insulator can be realized by condensing
vortices of a bo- son condensate. Usually, a vortex becomes an anti-vortex (and
vice-versa) under time reversal symmetry, and the condensation of vortices
results in a trivial Mott insulator. However, if each vortex or anti-vortex
interacts with a spin trapped at its core, the time reversal transformation of
the composite vortex operator will contain an extra minus sign. It turns out
that such a composite vortex condensed state is a bosonic topological insulator
(BTI) with gapless boundary excitations protected by $U(1)\rtimes Z_2^T$
symmetry. We point out that in BTI, an external $\pi$ flux monodromy defect
carries a Kramers doublet. We propose lattice model Hamiltonians to realize the
BTI phase, which might be implemented in cold atom systems or spin-1 solid
state systems.
