A Result in Surgery Theory

Abstract

AbstractWe study the topological 4-dimensional surgery problem for a closed connected orientable topological 4-manifold X with vanishing second homotopy and π1(X) ≅ A ∗ F(r), where A has one end and F(r) is the free group of rank r ≥ 1. Our result is related to a theorem of Krushkal and Lee, and depends on the validity of the Novikov conjecture for such fundamental groups.