2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125882Based on the U(1) gauge potential decomposition theory and the $ϕ$-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.6 pages, 0 figures, accepted by IJMPASuperconductivitytext