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In this paper, we introduce the notion of a virtual surface-knot as a 2-dimensional generalization of a virtual knot. We define the upper and lower groups of a virtual surface-knot to prove that there are infinitely many non-classical virtual surface-knots.
Ng constructed an invariant of knots in ℝ3, a combinatorial knot contact homology. Extending his study, we construct an invariant of surface-knots in ℝ4 using diagrams in ℝ3.