location:  Publications → journals → CMB
Abstract view

# A Result in Surgery Theory

Published:2008-12-01
Printed: Dec 2008
• Alberto Cavicchioli
• Fulvia Spaggiari
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

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.
 Keywords: four-manifolds, homotopy type, obstruction theory, homology with local coefficients, surgery, normal invariant, assembly map
 MSC Classifications: 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]