On 1-handle surgery and finite type invariants of surface knots (Q1612205)

In this paper, a surface knot is a closed connected surface (possibly non-orientable) which is generically immersed in 4-space. The author defines a local operation called 1-handle surgery and he proves that this operation is an unknotting operation for generically immersed surfaces in 4-space. (In fact, the author proves here a non-orientable version of an unknotting theorem for oriented surfaces which he had proved in his paper [Osaka J. Math. 36, No. 1, 33-49 (1999; Zbl 0930.57029)].) The author uses then the operation of 1-handle surgery to investigate finite type invariants (in the form of Vassiliev modules) for generically immersed surfaces in 4-space.