ON 4-MANIFOLDS HOMOTOPY EQUIVALENT TO SURFACE BUNDLES OVER SURFACES

被引：16

作者：

HILLMAN, JA ^{[1
]}

机构：

[1] UNIV SYDNEY,DEPT PURE MATH,SYDNEY,NSW 2006,AUSTRALIA

来源：

TOPOLOGY AND ITS APPLICATIONS | 1991年 / 40卷 / 03期

关键词：

EULER CHARACTERISTIC; 4-MANIFOLD; FUNDAMENTAL GROUP; KAPLANSKYS LEMMA; SURFACE BUNDLE; TOPOLOGICAL SURGERY; WHITEHEAD GROUP;

D O I：

10.1016/0166-8641(91)90110-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that a closed 4-manifold is homotopy equivalent to the total space of a surface bundle over a surface if the obviously necessary conditions on the fundamental group and Euler characteristic hold. When the base is the 2-sphere we need also conditions on the characteristic classes of the manifold. (Our results are incomplete when the base is the projective plane.) In most cases we can show the manifold is s-cobordant to the total space of the bundle.

引用

页码：275 / 286

页数：12

共 26 条

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