Cutting, pasting and the doubles of manifolds with boundary (Q2772938)

\(SK\) groups of manifolds are defined by cutting and pasting and one may create variants of this in other situations. One can form \(SK_m (\partial)\) for \(m\)-dimensional manifolds with boundary, \(SK_m^{Z_2}\) for manifolds with involution, or \(SK_{m,n}\) for \(m\)-dimensional manifolds with an \(n\)-dimensional submanifold. This paper shows that the operation from \(SK_m (\partial)\) into the \(SK\) group of manifolds with a codimension one submanifold obtained by forming the double factors through an \(SK\) group of manifolds with involution having a codimension one fixed set.