On the homotopy type of closed 4-manfolds covered by S2xR2

Author

Jonathan A. Hillman

Status

Research Report 96-22
Date: 17 April 1996

Topology and its Applications 75 (1997), 287-295

Abstract

We show that if M is a closed 4-manifold with nonpositive Euler characteristic and infinite cyclic second homotopy group then its homotopy type is determined up to a finite ambiguity by its fundamental group G. We also show that (for given G) the action of G on the second homotopy group and the orientation character determine each other, and find strong constraints on the possible k-invariants when the Euler characteristic of M is 0. Finally we show that the Whitehead group of G is trivial.

Key phrases

4-manifold. geometry. homotopy type. sphere bundle.

AMS Subject Classification (1991)

Primary: 57N13
Secondary: 55R10, 53C30

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