Georgia Institute of Technology College of Sciences

The classical Laudenbach-Poénaru theorem states that any diffeomorphism of $\#_n S^1 \times S^2$ extends over the boundary connect sum of $n$ $S^1 \times B^3$'s. This implies the familiar fact that in Kirby diagrams for closed 4 manifolds, you do not need to specify the attaching spheres for 3 handles; it is also the backbone result of trisection theory, which allows one to describe a closed 4 manifold by three cut systems of curves on a surface. We extend this result to the case of infinite 4-dimensional 1-handlebodies, with an eye towards developing trisections for noncompact 4 manifolds. The proof is geometric and based on extending the recent proof of Laudenbach-Poenaru due to Meier and Scott.