  We study the topological objects in two-component Bose-Einstein condensates.
We compare two competing theories of two-component Bose-Einstein condensate,
the popular Gross-Pitaevskii theory and the recently proposed gauge theory of
two-component Bose-Einstein condensate which has an induced vorticity
interaction. We show that two theories produce very similar topological
objects, in spite of the obvious differences in dynamics. Furthermore we show
that the gauge theory of two-component Bose-Einstein condensate, with the U(1)
gauge symmetry, is remarkably similar to the Skyrme theory. Just like the
Skyrme theory the theory admits the non-Abelian vortex, the helical vortex, and
the vorticity knot. We construct the lightest knot solution in two-component
Bose-Einstein condensate numerically, and discuss how the knot can be
constructed in the spin-1/2 condensate of $^{87}{\rm Rb}$ atoms.
