  Based on the U(1) gauge potential decomposition theory and the $\phi$-mapping
method, we study the vortex lines in two-gap superconductor and obtain the
condition, under which the vortices can carry an arbitrary fraction of magnetic
flux. It has been pointed out that the Chern-Simon action is a topological
invariant, which is just the total sum of all the self-linking numbers and all
the linking numbers of the knot family.
