A Result in Surgery Theory

Cavicchioli, Alberto ; Spaggiari, Fulvia

Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 508-518

Résumé

We study the topological 4-dimensional surgery problem for a closed connected orientable topological 4-manifold $X$ with vanishing second homotopy and ${{\pi }_{1}}\left( X \right)\,\cong \,A\,*\,F\left( r \right)$ , where $A$ has one end and $F\left( r \right)$ 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.

Détail

DOI : 10.4153/CMB-2008-051-x

Mots-clés : 57N65, 57R67, 57Q10, four-manifolds, homotopy type, obstruction theory, homology with local coefficients, surgery, normal invariant, assembly map

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