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TOPOLOGICAL 4-MANIFOLDS WITH GEOMETRICALLY TWO-DIMENSIONAL FUNDAMENTAL GROUPS

IAN HAMBLETON

Department of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada

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MATTHIAS KRECK

Hausdorff Research Institute for Mathematics, Poppelsdorfer Allee 82, D-53115 Bonn, Germany

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, and

PETER TEICHNER

Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720-3840, USA

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https://doi.org/10.1142/S1793525309000084Cited by:15 (Source: Crossref)

Abstract

Closed oriented 4-manifolds with the same geometrically two-dimensional fundamental group (satisfying certain properties) are classified up to s-cobordism by their w₂-type, equivariant intersection form and the Kirby–Siebenmann invariant. As an application, we obtain a complete homeomorphism classification of closed oriented 4-manifolds with solvable Baumslag–Solitar fundamental groups, including a precise realization result.

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