On the homotopy type of closed 4-manfolds covered by S2xR2
Jonathan A. Hillman
Research Report 96-22
Date: 17 April 1996
Topology and its Applications 75 (1997), 287-295
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.
4-manifold. geometry. homotopy type. sphere bundle.
AMS Subject Classification (1991)
Secondary: 55R10, 53C30
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