J Austral Math Soc Ser A 55 pp1--22, 1993.

Incompressible Surfaces and the Topology of 3-Dimensional Manifolds

Iain R. Aitchison and J. Hyam Rubinstein

Abstract

Existence and properties of incompressible surfaces in 3-dimensional manifolds are surveyed. Some conjectures of Waldhausen and Thurston soncerning 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 heirarchies 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.

1991 AMS Subject Classification: 57N10, 57M35, 57M50

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Authors

Iain R. Aitchison

Mathematics Department, University of Melbourne, Parkville, Victoria, Australia 3052.

J. Hyam Rubinstein

Mathematics Department, University of Melbourne, Parkville, Victoria, Australia 3052.