Three Kinds Of Invariants Of Long Virtual Links

In this paper,the univariate odd twist polynomials of directional virtual knots are extended to long virtual links.The bivariate exponential odd and even twist polynomials of long virtual links are given,and it is proved that they are invariants under generalized R-shift At the same time,this paper extends the Quandle and basic groups of virtual knots to long virtual links,defines Reidemeister and basic groups of long virtual links,and proves that they are invariants of Long virtual links under the generalized Reidemeister movement.