J. Aust. Math. Soc.
78 (2005), 305321

Normal surfaces in noncompact 3manifolds

Ensil Kang
Department of Mathematics
College of Natural Sciences
Chosun University
Gwangju 501759
Korea
ekang@chosun.ac.kr



Abstract

We extend the normal surface theory to noncompact 3manifolds with respect
to ideal triangulations. An ideal triangulation
of a 3manifold 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 noncompact
3manifold with an ideal triangulation with torus cusps can
be represented by a normal surface in as follows. A halfopen annulus made up of an
infinite number of triangular disks is attached
to each boundary component of
. The resulting surface
, 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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