Canad. Math. Bull. 51(2008), 508-518
Printed: Dec 2008
We study the topological $4$-dimensional surgery problem
for a closed connected orientable
topological $4$-manifold $X$ with vanishing
second homotopy and $\pi_1(X)\cong A * F(r)$, where $A$ has
one end and $F(r)$ is the free group of rank $r\ge 1$.
Our result is related to a theorem of Krushkal and Lee, and
depends on the validity of the Novikov conjecture for
such fundamental groups.
four-manifolds, homotopy type, obstruction theory, homology with local coefficients, surgery, normal invariant, assembly map
57N65 - Algebraic topology of manifolds
57R67 - Surgery obstructions, Wall groups [See also 19J25]
57Q10 - Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]