Topological Influence between Monopoles and Vortices: a Possible
  Resolution of the Monopole Problem
  Grand unified theories of fundamental forces predict that magnetic monopoles
are inevitable in the Universe because the second homotopy group of the order
parameter manifold is $\mathbb{Z}$. We point out that monopoles can annihilate
in pairs due to an influence of Alice strings. As a consequence, a monopole
charge is charactarized by $\mathbb{Z}_2$ rather than $\mathbb{Z}$ if the
Universe can accommodate Alice strings, which is the case of certain grand
unified theories.
