On 4-manifolds with universal covering space a compact geometric manifold

Journal of the Australian Mathematical Society

Jonathan A. Hillman¹ 

关键词: 57 N 13;   

DOI  :  10.1017/S1446788700032006

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

There are 11 closed 4-manifolds which admit geometries of compact type (S4, CP2 or S2 × S2) and two other closely related bundle spaces (S2 × S2 and the total space of the nontrivial RP2-bundle over S2). 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.

【 授权许可】

Unknown