Normal surfaces in topologically finite 3-manifolds

Details Normal surfaces in topologically finite 3-manifolds Normal surfaces in topologically finite 3-manifolds

2004-06-14

arxiv.org/abs/math/0406271v3

Mathematics

Geometric Topology

48 pages, 16 figures; completely re-written

Scientific paper

The concept of a normal surface in a triangulated, compact 3-manifold was generalised by Thurston to a spun-normal surface in a non-compact 3-manifold with ideal triangulation. This paper defines a boundary curve map which takes a spun-normal surface to an element of the direct sum of the first homology groups of the vertex linking surfaces. The boundary curve map is used to study the topology of a spun-normal surface as well as to determine the dimension of the projective solution space of the algebraic equations arising from the quadrilateral coordinates of spun-normal surfaces.

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