Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Four-Manifolds With Surface Fundamental Groups

Authors: Alberto Cavicchioli, Friedrich Hegenbarth and Dusan Repovs
Journal: Trans. Amer. Math. Soc. 349 (1997), 4007-4019
MSC (1991): Primary 57N65, 57R67, 57Q10
MathSciNet review: 1376542
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Abstract: We study the homotopy type of closed connected topological $4$-manifolds whose fundamental group is that of an aspherical surface $F$. Then we use surgery theory to show that these manifolds are $s$-cobordant to connected sums of simply-connected manifolds with an $\mathbb {S}^{2}$-bundle over $F$.

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Alberto Cavicchioli
Affiliation: Dipartimento di Matematica, Università di Modena, Via Campi 213/B, 41100 Modena, Italy

Friedrich Hegenbarth
Affiliation: Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy

Dusan Repovs
Affiliation: Institute for Mathematics, Physics and Mechanics, University of Ljubljana, P. O. Box 64, Ljubljana 61111, Slovenia

Keywords: Four-manifolds, homotopy type, $s$-cobordism, surgery, surface fundamental groups
Received by editor(s): January 20, 1995
Received by editor(s) in revised form: February 6, 1996
Additional Notes: Work performed under the auspices of the G.N.S.A.G.A. of the C.N.R. (National Research Council) of Italy and partially supported by the Ministero per la Ricerca Scientifica e Tecnologica of Italy within the projects “Geometria Reale e Complessa” and “Topologia” and by the Ministry for Science and Technology of the Republic of Slovenia Research Grant No. P1-0214-101-94.
Article copyright: © Copyright 1997 American Mathematical Society