Minimal Triangulations of Reducible 3-Manifolds

Details Minimal Triangulations of Reducible 3-Manifolds Minimal Triangulations of Reducible 3-Manifolds

2003-07-22

arxiv.org/abs/math/0307302v1

Mathematics

Geometric Topology

Ph.D. Dissertation, 136 pages

Scientific paper

In this thesis, we use normal surface theory to understand certain properties of minimal triangulations of compact orientable 3-manifolds. We describe the collapsing process of normal 2-spheres and disks. Using some geometrical constructions to take connected sums of triangulated 3-manifolds, we obtain the following result: given a minimal triangulation of a closed orientable 3-manifold M, it takes polynomial time in the number of tetrahedra to check if M is reducible or not.

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