On 1-handle surgery and finite type invariants of surface knots

Vassilievʹs 1-knot invariants are defined in a combinatorial way as finite type invariants. The notion of a finite type invariant associated with given local operations is defined. In this paper we prove that a local operation called a 1-handle surgery is an unknotting operation for generically immersed surfaces in 4-space and investigate the finite type invariants of such surfaces in 4-space associated with this operation.