Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 44, No. 1, pp. 189201 (2003) 

Decomposing FourManifolds up to Homotopy TypeAlberto Cavicchioli, Beatrice Ruini and Fulvia SpaggiariDipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, 41100 Modena, Italy; email: cavicchioli.alberto@unimo.itAbstract: Let $M$ be a closed connected oriented topological $4$manifold with fundamental group $\pi_1$. Let $\Lambda$ be the integral group ring of $\pi_1$. Suppose that $f : M\to P$ is a degree one map inducing an isomorphism on $\pi_1$. We give a homological condition on the intersection forms $\lambda^{\Bbb Z}_M$ and $\lambda^{\Lambda}_M$ under which $M$ is homotopy equivalent to a connected sum $P\# M'$ for some simplyconnected closed (nontrivial) topological $4$manifold $M'$. This gives a partial solution to a conjecture of Hillman [H] on the classification of closed $4$manifolds with vanishing second homotopy group. Then some splitting results for closed $4$manifolds with special homotopy complete the paper. [H] Hillman, J. A.: Free products and $4$dimensional connected sums. Bull. London Math. Soc. {\bf 27} (1995), 387391. Keywords: fourmanifolds, homotopy type, connected sum, obstruction theory, intersection forms, homology with local coefficients, degree one map Classification (MSC2000): 57N65, 57R67, 57Q10 Full text of the article:
Electronic version published on: 3 Apr 2003. This page was last modified: 4 May 2006.
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