Abstract
AbstractThere are 11 closed 4-manifolds which admit geometries of compact type (S4,CP2orS2×S2) and two other closely related bundle spaces (S2×S2and the total space of the nontrivialRP2-bundle overS2). We show that the homotopy type of such a manifold is determined up to an ambiguity of order at most 4 by its quadratic 2-type, and this in turn is (in most cases) determined by the Euler characteristic, fundamental group and Stiefel-Whitney classes. In (at least) seven of the 13 cases, a PL 4-manifold with the same invariants as a geometric manifold or bundle space must be homeomorphic to it.
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Schedule a callMore From: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
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