  We study the aqueous solution of vanadium pentoxide by using topology
methods. The experiments by Zocher, Kaznacheev, and Dogic exhibited, that in
the sol phases of $V_2O_5-H_2O$, the tactoid droplets of $V_2O_5$ can coalesce.
In the magnetic field, this effect is associated with a gauge field action,
viz. we consider coalescence (in the topologically more convenient term,
"junction") of droplets as annihilation of topological defects, concerning with
the tactoid geometry. We have shown, that in the magnetic field, the tactoid
junction is mainly caused by non-Abelian monopoles (vortons), whereas the
Abelian defects almost do not annihilate. Taking into account this annihilation
mechanism, the estimations of time-aging of the $V_2O_5-H_2O$ sols may be
specified
