On the intersection forms of closed 4-manifolds (Q1199340)

The authors study how the intersection form of a PL 4-manifold changes under a sequence of surgeries on curves that yield a simply connected manifold \(M^*\). The focus is on the case when the surgeries are on elements of finite order, with the result in this case being that the surgery adds copies of either \(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\) or \(\begin{pmatrix} 1 & 0 \\ 0 & -1\end{pmatrix}\) to the intersection form. Results of Donaldson and Freedman are then applied to determine the homeomorphism type of \(M^*\) under various hypotheses.