Incompressible surfaces and the topology of 3-dimensional manifolds

Journal of the Australian Mathematical Society

Iain R. Aitchison¹ 

[1] J. Hyam Rubinstein

关键词: 57 N 10;    57 M 35;    57 M 50;   

DOI  :  10.1017/S144678870003189X

学科分类：数学（综合）

来源: Cambridge University Press

【 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.

【 授权许可】

Unknown