We prove that the canonical 4–dimensional surgery problems can be solved after passing to a double cover. This contrasts the long-standing conjecture about the validity of the topological surgery theorem for arbitrary fundamental groups (without passing to a cover). As a corollary, the surgery conjecture is reformulated in terms of the existence of free involutions on a certain class of 4–manifolds. We consider this question and analyze its relation to the –slice problem.
"Surgery and involutions on 4–manifolds." Algebr. Geom. Topol. 5 (4) 1719 - 1732, 2005. https://doi.org/10.2140/agt.2005.5.1719