2 results
Normal surfaces in non-compact 3-manifolds
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 78 / Issue 3 / June 2005
- Published online by Cambridge University Press:
- 09 April 2009, pp. 305-321
- Print publication:
- June 2005
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- Article
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We extend the normal surface Q-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 Q-matching equations with a small number of variables. A unique feature of our approach is that a compact surface F with boundary properly embedded in a non-compact 3-manifold M with an ideal triangulation with torus cusps can be represented by a normal surface in M as follows. A half-open annulus made up of an infinite number of triangular disks is attached to each boundary component of F. The resulting surface
, when normalized, will contain only a finite number of Q-disks and thus correspond to an admissible solution to the system of Q-matching equations. The correspondence is bijective.
, when normalized, will contain only a finite number of Adjoint Linear Systems on Normal Log Surfaces
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- Journal:
- Compositio Mathematica / Volume 129 / Issue 1 / October 2001
- Published online by Cambridge University Press:
- 04 December 2007, pp. 47-66
- Print publication:
- October 2001
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