Normal surfaces in non-compact 3-manifolds

J. Aust. Math. Soc. 78 (2005), 305-321

Normal surfaces in non-compact 3-manifolds

Ensil Kang
Department of Mathematics
College of Natural Sciences
Chosun University
Gwangju 501-759
Korea
ekang@chosun.ac.kr

Abstract

We extend the normal surface

-theory to non-compact 3-manifolds with respect to ideal triangulations. An ideal triangulation of a 3-manifold often has a small number of tetrahedra resulting in a system of

-matching equations with a small number of variables. A unique feature of our approach is that a compact surface

with boundary properly embedded in a non-compact 3-manifold

with an ideal triangulation with torus cusps can be represented by a normal surface in

as follows. A half-open annulus made up of an infinite number of triangular disks is attached to each boundary component of

. The resulting surface $\hat{F}$ , when normalized, will contain only a finite number of

-disks and thus correspond to an admissible solution to the system of

-matching equations. The correspondence is bijective.

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