INCOMPRESSIBLE SURFACES AND THE TOPOLOGY OF 3-DIMENSIONAL MANIFOLDS

被引：9

作者：

AITCHISON, IR

RUBINSTEIN, JH

机构：

[1] Mathematics Department, University of Melbourne, Parkville

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS | 1993年 / 55卷

关键词：

D O I：

10.1017/S144678870003189X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Existence and properties of incompressible surfaces in 3-dimensional manifolds are surveyed. Some conjectures of Waldhausen and Thurston concerning such surfaces are stated. An outline is given of the proof that such surfaces can be pulled back by non-zero degree maps between 3-manifolds. The effect of surgery on immersed, incompressible surfaces and on hierarchies is discussed. A characterisation is given of the immersed, incompressible surfaces previously studied by Hass and Scott, which arise naturally with cubings of non-positive curvature.

引用

页码：1 / 22

页数：22

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